Jump to content

probability help

Recommended Posts

Help with this question:

using a 52 card pack, a 'royal flush' consists of the 10, J, Q, K A of one suit. Find the probability of dealing:

a. a royal flush in any order

b. a royal flush in the order 10, J, Q, K, A

 

ans:

a. 1.54 x 10^-6

b. 1.28 x 10^-8

Edited by allthebest

Share this post


Link to post
Share on other sites

a) P(RF, order does not matter) = combinations of royal flush of any of 4 suits / total dealing of 5 cards
b) P(RF, order matters) = permutations of royal flush of any of 4 suits / total dealing of 5 cards
nPk = permutations, nCk = combinations

a) P(RF) = 4 * (1 combo / suit) / (52 C 5) = 1.54 * 10^(-6)
b) P(RF) = 4 * (1 permutation / suit) / (52 P 5) = 1.28 * 10^(-8)

Note that answer a) is answer b) times 5!, or 120, or the factor from 52 5 to 52P5

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.