Question

Joe will randomly select two letters from the word camp, four letters from the word herbs, and three letters from the word glow. what is the probability that he will have all of the letters from the word problem? express your answer as a common fraction.

Answer 1

`(1)/(30)`

Explanation:

First we take the probability of the first one which is

`\frac{1}{ \binom{4}{2} }`

which is equal to 1/6

times 2/5

times 1/2

which is equal to 1/30

Answer 2

`|\Omega|=C(4,2)+C(5,4)+C(4,3)=(4!)/(2!2!)+(5!)/(4!)+(4!)/(3!)=6+5+4=15\\ |A|=3+2+2=7\\\\ P(A)=(7)/(15)`