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  • The total number of ways in which 6 pens of different colours can be distributed among 4 persons so that each person gets at least one pen.Option: 1

The total number of ways in which 6 pens of different colours can be distributed among 4 persons so that each person gets at least one pen.

Option: 1

1510


Option: 2

 1530


Option: 3

1560


Option: 4

1570

 


Answers (1)

best_answer

Given that,

The number of ways of distributing can be computed by the formula:
=r^{n}-\left(\begin{array}{l} r \\ 1 \end{array}\right)(r-1)^{n}+\left(\begin{array}{l} r \\ 2 \end{array}\right)(r-2)^{n}-\ldots+(-1)^{r-1}\left(\begin{array}{c} r \\ r-1 \end{array}\right)(1)^{n}
 

Number of pens, n=6
Number of person, r=4

Therefore, total number of ways

=4^{6}-\left(\begin{array}{l} 4 \\ 1 \end{array}\right)(4-1)^{6}+\left(\begin{array}{l} 4 \\ 2 \end{array}\right)(4-2)^{6}-\left(\begin{array}{l} 4 \\ 3 \end{array}\right)(4-3)^{6}
=4096-4(3)^{6}+6(2)^{6}-4(1)^{6}
=4096-2916+384-4
=1560



 

Posted by

Divya Prakash Singh

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