Question

13. There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?​

Answer 1

21/46

Step-by-step explanation:

Combinations of 3 students from among 25 = 25!/(22!)(3!) = 2,300.

Combinations of 1 girl (G) from among 10 girls = 10!(9!)(1!) =10.

Combinations of 2 boys (BB) from among 15 boys= 15!/(13!)(2!) = 105.

Combinations of 1 girl and 2 boys (GBB) = 10*105 = 1,050.

Probability as requested = 1,050/2,300 = 21/46 = .456521739…~ 45.7%.

You could also calculate the probability as (10/25)*(15/24)*(14/23)*](3!)/(2!)] = .456521739…~ 45.7%. The (3!)/2!) factor accounts for the number of ways of probability selection: GBB has 3! arrangements but the B’s are interchangeable.