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In how many ways can letters of the word BEHAVIOUR be arranged so that at most 2 vowels are together?

I considered 2 cases.

First case: All vowels are separated. I got 2880 ways.

Second case: 2 vowels are together. I cannot do it.

Please give me a clear explanation.

Thanks.

The letters of the word CURTAIN are arranged in a row. In how many ways can this be done if only 2 consonants are together??

The Answer is 1728.

It is difficult. Please Help.

Thanks.

Among 80 people attending a seminar consisting of a morning and and an evening sessions, 61 participated in the morning session and 43 in the afternoon session. Find:

(A) the greatest possible number of people who participated in one session only [I've got 43 buts the answer is 56]

(B) the least possible number of people who participated in one session only. [I've got 0 but answer is 18]

It is very confusing. Please if you can tell me also how the venn diagram would look like, i will be very grateful to you.

Please help me.

Thanks

1. The letters of the word CAMBRIDGE are arranged such that the first five letters of the alphabet are in alphabetical order. Find the number of different permutations. [ANS: 3024]

2. Two Families, each consisting of the father, the mother and a daughter, sit in a row. In how many ways can they be seated such that each arrangement is SYMMETRICAL with respect to

(a) the 2 fathers, the 2 mothers and the 2 daughters. [ANS=6]

(b) the 2 men, the 2 women, and the 2 girls. [ANS=48]

How is part (b) different from part (a)???

THANKS.

60 people were questioned about which of the colours red and blue they liked. & said they liked none, 28 did not like red and 30 did not like blue. By drawing a Venn diagram, find how many liked (a) blue only (b) both colours. [Ans. (a) 21 (b) 9]

Two players X and Y play a game in which X throws 6 coins and Y throws an unbiased die. Player X wins if the number of heads is greater than the number on the die.

The question is: If X throws 5 heads, find the probability that he wins.

THANKS

A painter has 4 benches to paint. He has paint of the following colours: RED, YELLOW, WHITE and BLACK. In how many ways can the benches be painted if

(a) he chooses the same colour

Answer 4

(b) at least one bench is of different colour

I've got 15 but the answer says 31???????

(c) all the benches are of different colours

Answer 1

(d) at least 2 benches should be painted red

I've got 11 but the answer says 10?????????

Well man, I trying hard with this problem...but two of my answers are wrong. Please check it.

A painter has 4 benches to paint. He has paint of the following colours: RED, YELLOW, WHITE and BLACK. In how many ways can the benches be painted if

(a) he chooses the same colour

Answer 4

(b) at least one bench is of different colour

I've got 15 but the answer says 31???????

(c) all the benches are of different colours

Answer 1

(d) at least 2 benches should be painted red

I've got 11 but the answer says 10?????????

THANKS MAN

REPLY as soon as possible please

Ok bye

A florist displays 5 different plants and 4 different ferns in a row. She decides to have only 2 flower plants and 2 ferns together. In how many ways can she do that?

PLEASE SHARE yr knowledge.

THANKS

Two families,each consisting of the father, the mother and a daughter, sit in a row. In how many ways can they be seated such that each arrangement is symmetrical with respect to

(a) the two fathers, the two mothers and the two daughters (show me the arrangements)

(b) the two men, the two women, and the girls???

PLEASE HELP

THANKS FRIENDS.

I'm totally new to this.

A van has 2 rows of 5 seats on each side. 5 married couples get on the van. In how many ways can they be seated if

(a) there is no restriction,

(b) the 5 wives are on the same side,

(c) each husband sits opposite his wife,

(d) each husband sits next to his wife except

(i) one couple (ii) one particular couple

for which, in each case, the husband and the wife sit opposite each other.

PLease frnds give me the good answers.

Next Question

5 married couples queue up to buy tickets for a show. In how many ways can they do so if

(a) there is no restriction

(b) the men queue up behind the women

(c) husband and wife are together.

(d) a man and a woman alternate?

Please explain me clearly.

THANKS

(1) Imagine yourself you had to explain type I and type II errors to a student who have just joined the world of statistics. (assuming the latter knows hypothesis testing)

please share all your effective ideas

(2)How to explain type I and type II errors through graphs(normal)??//???

(3)What is actually the significance level????

Two particles, X and Y, are moving on parallel horizontal tracks. At time t=0 both particles pass O (a fixed point). Both particles moves to the left of O. Velocity of X = 3 m/s and Acceleration of X = 5 m/s^2.

Velocity of Y = 7 m/s and Acceleration of Y = 2 m/s^2.

FIND;-

(1) the velocity of Y at the instant when X changes direction of motion.

My answer is 8.2 m/s. I found that X changes direction when t=(3/5) seconds.

(2) the time that elapses, from t=0, before both particles have the same velocity.

My thoughts:

I tried to sketch a velocity time graph for both particles. I guess for the two particles to have the same velocity, they should intersect. But then, particle Y is moving to the left and particle X to the right(changes direction of motion).

I solved for t by equating 2 equations. 3+5t = 7+2t , t = (4/3) but answers says (10/3) seconds.

I can't figure it out.

(3) the time that elapses from t=0, before X overtakes Y ???????????????????????

Please share all your valuable inputs/ideas.

THANKS IN ADVANCE.

I've been asked to state and justify my teaching philosophy.

What is this???? What does this mean????

My subject area is Physics......How to begin this problem???????

Please help me

Thanks friends.

If Applied force exceeds the Frictional force, then, the particle moves FORWARD.

That's right.

But, if Frictional force exceeds Applied force, does that mean:

(i) the particle slide BACKWARDS.

Or

(ii) the particle is still at rest.

I guest part (ii) is correct because Frictional force resists motion.

PLEASE Clear my confusion.

THANKS.

A particle of mass 0.5 kg lies on a rough plane inclined at an angle (alpha) to the horizontal, where sin(alpha) = (5/13).

The particle is acted on by a horizontal force of 8 N and is about to move up a line of greatest slope.

(a) Show that the value of the coefficient of friction between the particle and the plane is 0.71.

ANS: This part is alright. I got [(71/13)/(100/13)] = 0.71.

(b) Determine, with working, whether or not the particle will move when the force of 8 N is removed?????

ANS: I used F=ma. But then, can I allow the acceleration to be ZERO. Only then, I obtained Max Frictional Force = 5(sin alpha) = 5(5/13) = 25/13.

THEN, I see that Max Frictional Force < 0.71(Normal Contact Force = 60/13)

So, the particle does not move!

CAN I ALLOW THE ACCELERATION TO BE ZERO?????????????????????????

THAN KS

A particle of weight 45 N rests on a rough horizontal surface. A cord is attached to the particle and the particle is in limiting equilibrium when the tension in the cord is T newtons. The cord is in the "first quadrant" (just to give you an idea).

(A) Calculate the coefficient of friction and the magnitude of the contact force between the particle and the surface.

Ans: I do not know in which direction the particle is about to move. I cannot calculate the Normal contact force because the angle that the cord makes with the particle (with respect to the horizontal) is not given.

HOW TO Proceed???? ANSWER = 0.72 , 48N

(B) Calculate T and the angle between the cord and the horizontal???????

Ans: 29N , 12 degrees

PLEASE HELP ME OUT.

IF there are some tricks, explain 'em to me..

THANKS.