Five coupons of values $2,six coupons of values $3,two coupons of values $5 and two coupons of values $8 are put into a small box.Two coupons are drawn at random from the box without replacement.Calculate the probability that (b)the total value of two coupons is $10.

Question

[Answer:11over105]
What is the step?

Answer 1

Which ways can two of the 15 coupons total $10?

2+8
5+5
8+2

P(2,8) = 5/15 * 2/14 = 1/21
P(5,5) = 2/15 * 1/14 = 1/105
P(8,2) = 2/15 * 5/14 = 1/21

Add up the ways and you get 11/105