CMI2015-A-10

Question

The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners are placed is not considered. How many ways are there of choosing the team if the order of the runners is to be taken into account?

• A. Between $12,000$ and $25,000$
• B. Between $75,000$ and $99,999$
• C. Between $30,000$ and $60,000$
• D. More than $100,000$

Answer 1

Here are 3876 ways of choosing the team if the order in which the runners are placed is not considered.

Now No ways are there of choosing the team if the order of the runners is to be taken into account

Since here are 4 student they can be chosen in 4!=24 for the relay team.

So total No way in which order of the runners is to be taken into account

24*3876=93024

So it will be between Between 75,000 and 99,999.

Answer 2

Let us assume there are n students in the class.

Number of ways to choose a team of 4 members if the order in which the runners are placed is not considered =$\binom{n}{4}$.

=3876

Number of ways to choose a team of 4 members if the order in which the runners are placed is considered=n P 4 =$\binom{n}{4}$ *4!

=3876*24=93024.

Hence it will be between Between 75,000 and 99,999

 

Answer 3