Question

permutations 2.4 statistics answers A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra large. If it has 2 small, 3 medium, 6 large, and 2 extra large in stock, in how many orders can it sell all the shirts?

Answer 1

Answer: 360,360

Step-by-step explanation:

The number of permutations of n things of which a are identical, b are identical and so on... :-

$\dfrac{n!}{a!\ b!....}$

Given :  A clothing store has a certain shirt in 4 sizes: small, medium, large, and extra large.

If it has 2 small, 3 medium, 6 large, and 2 extra large in stock, then total shirts : $2+3+6+2=13$

Then, the number of orders in which the store can sell all the t-shirts will be :_

$\dfrac{13!}{2!3!6!2!}\\\\=\dfrac{13\times12\times11\times10\times9\times8\times7\times6!}{2\times3\times2\times6!\times2}\\\\=360360$

Hence, the number of orders in which the store can sell all the t-shirts  = 360,360