The number of ways a cricket team of 11 players can be chosen out of a total of 14 players can be calculated using the combination formula in mathematics.

The combination formula is: C(n, r) = n! / [(n-r)! * r!]

Where:
- n is the total number of options (in this case, 14 players),
- r is the number of options to choose (in this case, 11 players),
- "!" denotes a factorial, meaning the product of all positive integers up to that number.

So, substituting the given values into the formula:

C(14, 11) = 14! / [(14-11)! * 11!]

This simplifies to:

C(14, 11) = 14! / (3! * 11!)

Calculating the factorials:

= (14*13*12*11*10*9*8*7*6*5*4*3*2*1) / [(3*2*1) * (11*10*9*8*7*6*5*4*3*2*1)]

Many numbers can be cancelled out from the numerator and the denominator:

= (14*13*12) / (3*2*1)

= 364

So, there are 364 different ways a cricket team of 11 players can be chosen from a total of 14 players.

Question

The number of ways a cricket team of 11 players can be chosen out of a total of 14 players can be calculated using the combination formula in mathematics.

The combination formula is: C(n, r) = n! / [(n-r)! * r!]

Where:
- n is the total number of options (in this case, 14 players),
- r is the number of options to choose (in this case, 11 players),
- "!" denotes a factorial, meaning the product of all positive integers up to that number.

So, substituting the given values into the formula:

C(14, 11) = 14! / [(14-11)! * 11!]

This simplifies to:

C(14, 11) = 14! / (3! * 11!)

Calculating the factorials:

= (14*13*12*11*10*9*8*7*6*5*4*3*2*1) / [(3*2*1) * (11*10*9*8*7*6*5*4*3*2*1)]

Many numbers can be cancelled out from the numerator and the denominator:

= (14*13*12) / (3*2*1)

= 364

So, there are 364 different ways a cricket team of 11 players can be chosen from a total of 14 players.

Knowee AI · Accepted Answer