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Question

Mathematics Question on permutations and combinations

A sports team of 1111 students is to be constituted, choosing atleast 55 from class and atleast 55 from Class If there are 2020 students in each of these classes, in how many ways can the team be constituted?

A

20× 20C520 \times \, ^{20}C_{5}

B

20C5× 20C6^{20}C_{5} \times\, ^{20}C_{6}

C

2× 20P5× 20P62\times\, ^{20}P_{5} \times\, ^{20}P_{6}

D

2× 20C5× 20C62\times\,^{20}C_{5} \times\, ^{20}C_{6}

Answer

2× 20C5× 20C62\times\,^{20}C_{5} \times\, ^{20}C_{6}

Explanation

Solution

No. of students in each class =20= 20 We have to select atleast 55 students from each class. ∴\therefore No. of selection of sports team of 1111 students from each class is given in following table. ∴\therefore Total number of ways of selecting a team of 1111 players =(20C5× 20C6)+ (20C6× 20C5)=(^{20}C_{5} \times\, ^{20}C_{6}) +\, (^{20}C_{6} \times\, ^{20}C_{5}) =2× 20C5× 20C6= 2\times\, ^{20}C_{5} \times\,^{20}C_{6}