Puzzling
Problem 1:
Use the fundamental counting principle.
https://www.mathsisfun.com/data/basic-counting-principle.html
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.