Question

Out of 16 men , in how many ways a group of 7 men may be selected so that:(i) particular 4 men will not come,. (ii) particular 4 men will always come ? Chp:- combination. Plz answer .

Answer 1

hope it helps you out dude

Answer 2

i)  Number of ways to select 7 men when particular 4 men will not come = 792

ii) Number of ways to select 7 men when particular 4 men will always come = 220

Explanation:

Total men = 16

Number of men needed to be selected for a group = 7

i) particular 4 men will not come

Then, the total choices left = 16-4= 12

Number of combination of 7 men from 12 = $^{12}C_7$

$=\dfrac{12!}{7!(12-7)!}\\\\=792$

∴  Number of ways to select 7 men when particular 4 men will not come = 792

ii) particular 4 men will always come

Then, the number of men we need to select more = 7-4=3

Total choices left = 12

Number of combination of 7 men from 12 = $^{12}C_3$

$=\dfrac{12!}{3!(12-3)!}\\\\=220$

∴  Number of ways to select 7 men when particular 4 men will always come = 220

# Learn more :

Out of 5 ladies and 3 gentleman , a committee of 6 is to be selected. In how many ways can this be done :-(i) when there are 4 ladies, (ii) when there is a majority of ladies? Plz,plz answer. Chp:- combination

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