Question

# Title A standard deck of cards consisting of 52 cards, 13 in each of 4 different suits, is shuffled, and   Description ...

Title
A standard deck of cards consisting of 52 cards, 13 in each of 4 different suits, is shuffled, and

Description
A standard deck of cards consisting of 52 cards, 13 in each of 4 different suits, is shuffled, and 4 cards are drawn without replacement. What is the probability that all four cards are of a different suit?

Given

A standard deck of cards consisting of 52 cards, 13 in each of 4 different suits, is shuffled

Number of ways 4 cards can be drawn from a deck of cards

$={52}_{{C}_{4}}\phantom{\rule{0ex}{0ex}}=270725$

Again, there are 4 suits of 13 cards each.

So the number of ways 4 cards from different suits can be drawn

$={13}_{{C}_{1}}×{13}_{{C}_{1}}×{13}_{{C}_{1}}×{13}_{{C}_{1}}\phantom{\rule{0ex}{0ex}}=28561$

So the probability is

$\frac{28561}{270725}\phantom{\rule{0ex}{0ex}}=0.105$

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