What is the probability of being dealt 3 tens and 2 kings from a deck of cards?

We need to find the probability of getting 3 tens and 2 kings

First we find possible combinations of selecting 5 cards from 52 cards

That is 52C5

We use formula n!/ r!(n-r)!

52!/ 5!(52-5)! = 2598960

In 52 cards, we have 4 tens and 4 kings

We need to select 3 tens from 4 tens

So we find 4C3 = 4!/ 3!(4-3)! = 4

We need to select 2 kings from 4 kings

So we find 4C2 = 4!/ 2!(4-2)! = 6

The probability of 3 tens and 2 queens = (4C3 * 4C2) / 52C5

(4*6)/ 2598960 = 1/108290

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