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 :-
(a) 380
(b) 320
(c) 260
(d) 95
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Answers
Answer:
Option(a)
Step-by-step explanation:
At most 1 boy = No boy, 1 boy.
Total number of girls = 6.
Total number of boys = 4.
(i) Selecting 1 boy and 3 girls:
Selecting 1 boy and 3 girl = C(4,1) * C(6,3)
= 4 * 20
= 80
Selecting a captain = 1 + C(3,1)
= 1 + 3
= 4.
Number of ways = 80 * 4 = 320.
(ii) Selecting No boy, 4 girls:
Selecting 4 girls = C(6,4)
= 15
Selecting captain = C(4,1)
= 4
Number of ways = 15 * 4
= 60.
∴ Number of ways of selecting the team:
= 320 + 60
= 380.
Hope it helps!
Answer:
Total no. Of ways of selection of team = (1 boy and 3 girls)(selection of captain) + ( 0 boy and 4 girls) ( selection of captain)
=4C1*6C3*(4C1) + 6C4*4C0*(4C1)
=320+60
=380 ways
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