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Standard XI

Mathematics

Properties of Set Operation

A sports team...

Question

A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?

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Solution

A sports team of 11 students is to be constituted, choosing at least 5 students of class XI and at least 5 from class XII.
Required number of ways = $^{20} C_{5} \times^{20} C_{6} +^{20} C_{6} \times^{20} C_{5} = 2 \times^{20} C_{5} \times^{20} C_{6} = 2 (20_{C_{6}} \times 20_{C_{5}})$

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Similar questions

A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted ?

Q. A sports team of 11 students is to be constituted choosing at least 5 from class IX and at least 5 from class X. If there are 8 students in each of these classes, in how many ways can the team be constituted?

Q. There are

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Q. There are

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Q. In how many ways a team of 11 be chosen from 20 students of a class so that 2 particular students are alwayts included and 5 are always excluded?

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A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?

A sports team of 11 students is to be constituted, choosing at least 5 students of class XI and at least 5 from class XII. Required number of ways = 20C5×20C6 + 20C6×20C5 = 2 ×20C5×20C6 = 2 20C6 × 20C5

A sports team of 11 students is to be constituted, choosing at least 5 students of class XI and at least 5 from class XII.
Required number of ways = $^{20} C_{5} \times^{20} C_{6} +^{20} C_{6} \times^{20} C_{5} = 2 \times^{20} C_{5} \times^{20} C_{6} = 2 (20_{C_{6}} \times 20_{C_{5}})$