Answer :

There are 20 students in each classes and there is need of at least 5 students in each class to form a team of team of 11.

Now,

There are two ways in which the selection can be possible

1. Selecting 5 from XI and 6 from XII

2. Selecting 6 from XI and 5 from XII

Now, considering first case ,

No. of ways in selection of 5 students from 20 in class XI = ^{20}C_{5}

No. of ways in selection of 6 students from 20 in class XII = ^{20}C_{6}

By multiplication principle total no. of ways in first case is

= ^{20}C_{5} ^{20}C_{6}

Now, considering second case,

No. of ways in selection of 6 students from 20 in class XI = ^{20}C_{6}

No. of ways in selection of 5 students from 20 in class XII = ^{20}C_{5}

By multiplication principle total no. of ways in second case is

= ^{20}C_{6} ^{20}C_{5}

Now the total no. of ways will be the addition of both the cases

= = ^{20}C_{5} ^{20}C_{6} + ^{20}C_{6} ^{20}C_{5}

= 2 ^{20}C_{6} ^{20}C_{5}

Thus these are the ways by which A sports team of 11 students is to be constituted

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