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How many times each of the prizes listed below will be given to a group of 7 employees: first and second for dancing, first and second for singing, first in the debate, and first in mimicry?

Option: 1

72360


Option: 2

86436


Option: 3

91356

 


Option: 4

63436


Answers (1)

best_answer

Given that,

There are 7 employees in a company.

The first prize for dancing can be given in 7 ways.

The first prize for singing can be given in 7 ways.

The first prize for debate can be given in 7 ways.

The first prize for mimicry can be given in 7ways.

There are 4 first prizes which can be given in 10^{4}ways.

Thus,

\begin{aligned} &7^4=7 \times 7 \times 7 \times 7\\ &7^4=2401 \end{aligned}

Since an employee cannot get the first and second prize together, the second prize is given in 6^2 ways.

Thus,

\begin{aligned} &6^2=6 \times 6\\ &6^2=36 \end{aligned}

So, the total number of required ways is given by,

\begin{aligned} &7^4 \times 6^2=2401 \times 36\\ &7^4 \times 6^2=86436 \end{aligned}

Therefore, the required number of ways is 86436.

Posted by

manish painkra

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