In how many ways can a cricket team of 11 players be chosen out from a squad of 14 players, if 5 particular players are always chosen?a)84b)144c)1001d)1365Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Total no of players = 14 out of which 5 are fixed.
So, 11-5 = 6
Remaining players = 14 - 6
= 9 players
9C6 = 9!/(3!*6!)
= 84

Answer

84

Answer

Subtract Fixed No. of Players(5) from the No. of people playing in the team(11) and then multiply it from the total no. people (14).

It will be:

11-5=6

6*14=84

Answer

Answer

Cricket team total no players = 11.  ......lless 11 --5=6......6×14= 84

Answer

To solve this problem, we can use the concept of combinations.

Step 1: Selecting the 5 particular players
Since 5 particular players are always chosen, we do not need to consider them when calculating the number of ways to choose the remaining 6 players. Therefore, we need to select 6 players out of the remaining 14 - 5 = 9 players.

Step 2: Selecting the remaining 6 players
To select the remaining 6 players, we need to calculate the number of combinations of 9 players taken 6 at a time. This can be calculated using the formula for combinations:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of players to choose from and r is the number of players to be chosen.

In this case, n = 9 and r = 6. Substituting these values into the formula, we get:

C(9, 6) = 9! / (6! * (9 - 6)!)
= 9! / (6! * 3!)
= (9 * 8 * 7 * 6!) / (6! * 3!)
= (9 * 8 * 7) / (3 * 2 * 1)
= 84

Step 3: Calculate the total number of ways
Now that we know there are 84 ways to choose the remaining 6 players, we need to consider the 5 particular players that are always chosen. These players have already been selected, so we do not need to consider them when calculating the total number of ways.

Therefore, the total number of ways to choose a cricket team of 11 players from a squad of 14 players, with 5 particular players always chosen, is 84.

Therefore, the correct answer is option A) 84.

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