Permutation and Combination Qn?

the number of possible pairings is n!

let's assume the male picks the female for the pairing

when you begin, the first male has n females to choose from.

after he has taken, the next male has n-1 females to choose from, and so on until the last couple, where the male only has 1 female to choose from.

if you test it with the cases n=2 and n=3, you will see that the number of pairings is 2 and 6, respectively.

(1,2) with (A,B) ==> {(1,A), and (2,B)}, {(1,B), and (2,A)}

When you have n independent choices of things, and you select them k times, the number of combinations is n^k.

It's like a combination lock: suppose its numbers go from 1 to 60, and the combination has 3 numbers in it. For the first number, there are 60 possibilities; for the second number, there are 60 possibilities for each possibility of the first number; for the third number, there are 60 possibilities for each possibility of the second number. This is 60 choices made 3 times, so the total is 60³ = 216,000.

A car's odometer is the same way, with 10 possibilities per dial for each dial to the left of the right-hand end.

So, for each of n males, there are n choices of female partner; this is selecting n items twice, so the total is n².

a. So there are 25 total students and you want to get 4 male students...that means order matters since you have to pick males 4 times in a row. Since order matters it would be nPr with n = 25 and r = 4. b. In this one, order doesn't matter so it is nCr with n = 25 and r = 6. Just plug this into your TI-8++ to get the answers.

ans will be n*n

explanation: for every male there are n possible females.so for every male n pairings is possible.

Now there are n males so total number of pairings for n males = n*n.thus n*n is the answer .Take for example n=2..in that case 4 pairings are possible u can check very easily