Math Questions please help ?

Problem 1:

Use the fundamental counting principle.

https://www.mathsisfun.com/data/basic-counting-pri...

Problem 2:

Use the C(n,k) formula for the ways from n items to pick k of them:

C(n,k) = n! / ((n-k)! k!)

From the 5 teachers, pick 2

C(5,2) = (5 * 4) / (2 * 1) = 10 ways

From the 6 students, pick 3:

C(6,3) = (6 * 5 * 4) / (3 * 2 * 1) = 20 ways

Multiply the two together to get the total ways of picking 2 teachers and 3 students.

Problem 3:

Similar to #2, calculate C(14,3)

C(14,3) = (14 * 13 * 12) / (3 * 2 * 1)

Problem 4:

There are 13 cards in each suit (so there are 13 diamonds) out of 52 cards.

P(diamond) = 13/52

Reduce the fraction and convert it to a decimal.