Question

Let $X$ be the set of all five-digit numbers formed using $1,2,2,2,2,4,4,0$. for example $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that a component chosen at random is a multiple of $20$ given that it is a multiple of $5$. Then the numerous of $38p$ is equal to

Answer 1

Count of five-digit numbers ending with 0 and divisible by 5 and 20 = 38 - 7 = 31.

So, the answer is 31.