You visited us 2 times! Enjoying our articles? Unlock Full Access!

Maximum Value of nCr

In a touring ...

Question

In a touring cricket team there are $16$ players in all including $4$ bowlers and $2$ wicket-keepers, How many teams of $11$ players from these, can be chosen , so as to include three bowlers and one wicket-keeper

650

No worries! We‘ve got your back. Try BYJU‘S free classes today!

720

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

750

No worries! We‘ve got your back. Try BYJU‘S free classes today!

800

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $720$
$\begin{matrix} T h e r e a r e 4 b o w l e r s 2 w i c k e t - k e e p e r s 10 n o n - b o w l e r s n o t w i c k e t k e e p e r s . C a s e A T h e r e a r e e x a c t l y 3 b o w l e r s, e x a c t l y 1 w i c k e t k e e p e r, a n d 7 n o n - b o w l e r s n o n w i c k e t k e e p e r s .^{3} C_{1} \times^{2} C_{1} \times^{10} C_{7} = 960 C a s e B T h e r e a r e e x a c t l y 4 b o w l e r s, e x a c t l y 2 w i c k e t k e e p e r, a n d 6 n o n - b o w l e r s n o n w i c k e t k e e p e r s .^{4} C_{3} \times^{2} C_{2} \times^{10} C_{6} = 840 C a s e C T h e r e a r e e x a c t l y 4 b o w l e r s, e x a c t l y 1 w i c k e t k e e p e r, a n d 6 n o n - b o w l e r s n o n w i c k e t k e e p e r s .^{4} C_{4} \times^{2} C_{1} \times^{10} C_{6} = 420 C a s e D T h e r e a r e e x a c t l y 4 b o w l e r s, e x a c t l y 2 w i c k e t k e e p e r, a n d 5 n o n - b o w l e r s n o n w i c k e t k e e p e r s .^{4} C_{4} \times^{2} C_{2} \times^{10} C_{5} = 252 N o w, T o t a l n u m b e r s o f w a y s = 960 + 840 + 420 + 252 = 2472 H e n c e, t o t a l n u m b e r o f w a y s i s 2472. \end{matrix}$
Hence,option $B$ is the correct answer.

Suggest Corrections

Similar questions

16

4

2

11

3

1

16

2

5

1

4

16

4

2

11

3

1

25

10

8

5

2

11

5

3

2

1

Join BYJU'S Learning Program