Question

In how many ways can a cricket eleven be chosen out of a batch of $15$ players if there is no restriction on the selection?

• A. ${}^{15}{C}_0$
• B. ${}^{15}{C}_1$
• C. ${}^{15}{C}_{11}$
• D. None of these

Answer 1

Answer: (C)

${}^{15}{C}_{11}$

Total number of ways of selecting $11$ players out of $15$ is,

$={}^{15}{C}_{11}$................$\left(Intheformof{}^n{C}_r\right)$

$={}^{15}{C}_{15-11}$

$={}^{15}{C}_4$

$=\frac{15\times 14\times 13\times 12}{4\times 3\times 2\times 1}$................$(Usingformulaof{}^n{C}_r=\frac{n!}{r!(n-r)!})$

$=1365$

Hence option-$C$.