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  • How many times each of the following prizes will be awarded to a class of 10 students: first and second in science, first and second in Mathematics, first in Chemistry and first in English.

How many times each of the following prizes will be awarded to a class of 10 students: first and second in science, first and second in Mathematics, first in Chemistry and first in English.

 

Option: 1

360000


Option: 2

490000


Option: 3

640000


Option: 4

810000


Answers (1)

best_answer

Given that,

There are 10 students in a class.

The first prize for science can be given in 10 ways.

The first prize for Mathematics can be given in 10 ways.

The first prize for chemistry can be given in 10 ways.

The first prize for English can be given in 10 ways.

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

Thus, 

\begin{aligned} & 10^4=10 \times 10 \times 10 \times 10 \\ & 10^4=10000 \end{aligned}

Since a student cannot get the first and second prize together, the second prize is given in 9^{2} ways.

Thus,


\begin{aligned} & 9^2=9 \times 9 \\ & 9^2=81 \end{aligned}

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

\begin{aligned} & 10^4 \times 9^2=10000 \times 81 \\ & 10^4 \times 9^2=810000 \end{aligned}

Therefore, the required number of ways is 810000.

 

 

 

Posted by

Ritika Kankaria

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