A sports team of $11$ students is to be constituted, choosing atleast $5$ from class and atleast $5$ from Class If there are $20$ students in each of these classes, in how many ways can the team be constituted?
Updated On: Jul 6, 2022
$20 \times \, ^{20}C_{5}$
$^{20}C_{5} \times\, ^{20}C_{6}$
$2\times\, ^{20}P_{5} \times\, ^{20}P_{6}$
$2\times\,^{20}C_{5} \times\, ^{20}C_{6}$
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The Correct Option isD
Solution and Explanation
No. of students in each class $= 20$
We have to select atleast $5$ students from each class.
$\therefore$ No. of selection of sports team of $11$ students from each class is given in following table.
$\therefore$ Total number of ways of selecting a team of $11$ players
$=(^{20}C_{5} \times\, ^{20}C_{6}) +\, (^{20}C_{6} \times\, ^{20}C_{5}) $$= 2\times\, ^{20}C_{5} \times\,^{20}C_{6}$
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
Combination refers to the combination of about n things taken k at a time without any repetition.
The combination is used for a group of data where the order of data does not matter.
