Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.5 - Generalized Permutations and Combinations - Exercises - Page 433: 42

Answer

$\frac{52!}{13!^{4}}$ = 53,644,737,765,488,792,839,237,440,000

Work Step by Step

Each player will receive 13 cards Here n=52 k=4 $n_{1}$=13 $n_{2}$=13 $n_{3}$=13 $n_{4}$=13 Distributing n distinguishable objects into k distinguishable boxes such that $n_{i}$ objects are there in each box can be done in $\frac{n!}{x_{1}!....x_{k}!}$ ways. In our case $\frac{52!}{13!^{4}}$ = 53,644,737,765,488,792,839,237,440,000
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