You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Combination with Restrictions

A debate club...

Question

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is -

380

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

320

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

260

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

Open in App

Solution

The correct option is A 380
Either one boy will be seleted or no boy will be selected. Also out of four members one captain is to be selected.
$∴$ Required number of ways = $(^{4} C_{1} \times^{6} C_{3} +^{6} C_{4}) \times^{4} C_{1}$
= $(80 + 15) \times 4$ = 380

Suggest Corrections

Similar questions

Q. A debate club consists of

6

girls and

4

boys. A team of

4

members is said to be selected from this club including the selection of a captain (from among these

4

members) for the team. If the team has to be include at most one boy, then the number of ways of selecting the team is

Q. A group consists of

4

girls

& 7

boys, In how many ways can a team of

5

members be selected if the team has "at least one boy

&

one girl?

a group consist of 4 girls and 7 boys in how many ways can a team of 5 members be selected if the team has 1) no girl 2)atlest one boy and one girl 3)at least 3 girls

Q. A group consists of

4

girls and

7

boys. In how many on a team of

5

members be selected, if the team has
(i) No girl.
(ii) at least one boy and one girl.
(iii) at least three girls.

Q. There are

15

members in a cricket club out of which

7

are batsmen,

6

are bowlers and

2

are wicket-keepers. A team of

11

players is to be formed from these

15

members. If the coach decides to include at least

4

batsmen and

1

wicket-keeper in the team, then the number of ways in which the team can be selected is

Join BYJU'S Learning Program

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is -

The correct option is A 380Either one boy will be seleted or no boy will be selected. Also out of four members one captain is to be selected. ∴ Required number of ways =( 4C1× 6C3+ 6C4)× 4C1 = (80+15)×4 = 380

The correct option is A 380
Either one boy will be seleted or no boy will be selected. Also out of four members one captain is to be selected.
$∴$ Required number of ways = $(^{4} C_{1} \times^{6} C_{3} +^{6} C_{4}) \times^{4} C_{1}$
= $(80 + 15) \times 4$ = 380