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In how many ways can 3 peaches, 2 tangerines, 4 mangos, and 1 apple be given to 10 children if each child receives exactly 1 piece of fruit?12,60025,20028824

In How Many Ways Can 3 Peaches 2 Tangerines 4 Mangos And 1 Apple Be Given To 10 Children If Each Child Receives Exactly 1 Piece Of Fruit126002520028824 class=

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STEP - BY - STEP EXPLANATION

What to find?

Number of ways 3 peaches, 2 tangerines, 4 mangos, and 1 apple can be given to 10 children if each child receives exactly 1 piece of fruit.

Given:

Number of children = 10

Number of peaches = 3

Number of tangerines = 2

Number of Mangoes = 4

Number of apple = 1

Choices of peaches = 3!

Choices of tangerines = 2!

Choices of mangoes = 4!

Choice of apple = 1!

[tex]Number\text{ of ways=}\frac{10!}{3!\times2!\times4!\times1!}[/tex][tex]=\frac{10\times9\times8\times7\times6\times5\times4!}{3\times2\times2\times1\times4!\times1}[/tex][tex]=\frac{10\times9\times8\times7\times5}{2}[/tex][tex]12600[/tex]

ANSWER

12600

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