Number of Permutations/Examples/4 from 52

Example of Number of Permutations

The number of ways of choosing $4$ objects in order from a set of $52$ (for example, cards from a deck) is:

${}^{52} P_4 = 52 \times 51 \times 50 \times 49 = \dfrac {52!} {48!} = 6 \, 497 \, 400$

Proof

From Number of Permutations:

${}^{52} P_4 = \dfrac {52!} {\paren {52 - 4}!}$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$