Question:

In how many ways can a football team of $11$ players be selected from $16$ players? How many of them will (i) include $2$ particular players? (ii) exclude $2$ particular players?

Updated On: Jul 6, 2022
  • $^{16}C_{9}, \,^{14}C_{11}$
  • $^{14}C_{9}, \,^{14}C_{11}$
  • $^{14}C_{9}, \,^{16}C_{11}$
  • None of these
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The Correct Option is B

Solution and Explanation

Total number of players = $16$ $\therefore$ No. of ways of selecting $11$ players out of $16$ players $ = \,^{16}C_{11}$ . (i) If $2$ particular players are included then number of ways $ = \,^{16-2}C_{2} = \,^{14}C_{9}$ (ii) If $2$ particular players are excluded then number of ways $ = \,^{16-2}C_{11} = \,^{14}C_{11}$
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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.