Five cards are dealt at random from a deck of 52 playing car

Five cards are dealt at random from a deck of 52 playing cards. Find the probability that three of them are sevens.

Please show your work.

Solution

Five cards are dealt at random from a deck of 52 playing cards. Find the probability that three of them are sevens.

This is a combination problem.

Number of ways 5 cards from 52 cards =52C5

We want 3 of the 4 sevens

Number of ways 3 sevens from 4 sevens= 4C3

Number of ways remaining 2 cards from remaining 48 cards =48C2

P(3 sevens) = (4c3)*(48c2) / (52c5)

= 0.001736