Combinatorics and Counting Flashcards

What is the probability of getting a sum of 7 when two dice are rolled?

Answer: 6/36

Combinations that give 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — 6 out of 36 total outcomes = 6/36 = 1/6.

Using the letters A, B, C, D, E, how many 3-letter arrangements can be made without repetition?

Answer: 60

P(5,3) = 5!/(5−3)! = 5 × 4 × 3 = 60.

A jar has 4 green, 3 yellow, and 3 red candies. What is the probability of randomly picking a green candy?

Answer: 2/5

Total candies = 10; P(green) = 4/10 = 2/5.

How many different 3-digit numbers can be formed from 1, 2, 3, 5, 7 without repetition?

Answer: 60

P(5,3) = 5 × 4 × 3 = 60.

If C(n, 2) = 15, what is n?

Answer: 6

C(n,2) = n(n−1)/2 = 15 → n(n−1) = 30 → n = 6 (since 6 × 5 = 30).

Two cards are drawn from a standard 52-card deck without replacement. How many ways can both cards be aces?

Answer: 6

C(4,2) = 4!/(2! × 2!) = (4 × 3)/(2 × 1) = 6.