Calculate the number of outcomes

)!(!

!

rnr

n

r

n

We can calculate the number of possible outcomes instead of making a list, by using a formula.

n = total

r = total number chosen

r

ncan also be written as nCr.

Example

3 cards are dealt from an ordinary pack of playing cards.

a) Calculate the probability that 3 kings are dealt.

b) Calculate the probability that 2 jacks and 1 queen are dealt.

We must first calculate the total number of combinations of choosing 3 cards.52C3 = 22100

(This is the denominator throughout the question.)

b) Deal 2 jacks and 1 queen = 4C2 x 4C1 = 24

P(Deal 2 jacks and 1 queen) = 24 . = 6

22100 5525

a) Ddeal 3 kings = 4C3 = 4

P(deal 3 kings) = 4 . = 1 . 22100 5525