In how many ways can 12 balls be divided between 2 boys, one receiving 5 and the other 7 balls?

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Solution

Here order is important, then the number of ways in which 12 different balls can be divided balls can be divided between two boys which contains 5 and 7 balls respectively, is
= $\frac{12!}{5! 7!} \times 2!$
= $\frac{12.11.10.9.8.7!}{(5.4.3.2.1) 7!} \times 2 = 1584$

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In how many ways can 12 balls be divided between 2 boys, one receiving 5 and the other 7 balls? ___

Here order is important, then the number of ways in which 12 different balls can be divided balls can be divided between two boys which contains 5 and 7 balls respectively, is =12!5!7!×2! =12.11.10.9.8.7!(5.4.3.2.1)7!×2=1584

In how many ways can 12 balls be divided between 2 boys, one receiving 5 and the other 7 balls?

___

Here order is important, then the number of ways in which 12 different balls can be divided balls can be divided between two boys which contains 5 and 7 balls respectively, is
= $\frac{12!}{5! 7!} \times 2!$
= $\frac{12.11.10.9.8.7!}{(5.4.3.2.1) 7!} \times 2 = 1584$