There are 4 cardio stations and six weight lifting stations at the gym. You decide to chose 4 stations randomly for today's workout. Whats the probability that you choose all weight lifting or all cardio?

Answer 1

I assume you never use the same machine twice

first cardio = 4/10 = 2/5
second = 3/9 =1/3
third = 2/8 = 1/4
fourth = 1/7

product = 2/5 *1/3*1/4*1/7

= 1/210
now weight
first =6/10 = 3/5
second = 5/9
third = 4/8 = 1/2
fourth = 3/7
product = 3/5 * 5/9 * 1/2 * 3/7
=1/14
so
1/210 + 1/14 =1/210 + 15/210
= 16/210
= 8/105 = .0762