Question

In a bag of m&m's there are 5 brown 6 yellow 4 blue 3 green and 2 orange. What's the probability of getting 3 yellow m&m's if 3 are taken at a time?

Answer 1

There are 5+6+4+3+2=20 m&m's in the bag.
Calculate in how many ways you can choose 3 m&m's from 20:

`_(20) C _3=(20!)/(3!(20-3)!)=(20!)/(3! * 17!)=(17! * 18 * 19 * 20)/(6 * 17!)=(18 * 19 * 20)/(6)=3 * 19 * 20= \\ =1140`

There are 6 yellow m&m's.
Calculate in how many ways you can choose 3 m&m's from 6:

`_6 C _3 = (6!)/(3!(6-3)!)=(6!)/(3! * 3!)=(3! * 4 * 5 * 6)/(3! * 6)=(4 * 5 * 6)/(6)=4 * 5=20`

The probability is the number of ways of choosing 3 m&m's from 6 m&m's divided by the number of ways of choosing 3 m&m's from 20 m&m's.

`P= (20)/(1140)=(20 / 20)/(1140 / 20)=(1)/(57)`

The probability is 1/57.