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Number of ways in which committee can be formed – SNAP 2013 Question

Q.)The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is
(a) 1960
(b) 3240
(c) 1540
(d) None of these

[SNAP 2013 Question , SNAP Questions , Permutations and Combinations]
Solution :

Case I : When Mr. Y is included in the committee :

Then , we need to select 3 ladies from 7 ladies and 3 gentlemen from 6 gentlemen as Y is included and Mrs. X refuses to be in committee.

No of ways = { 7 }_{ { C }_{ 3 } }*{ 6 }_{ { C }_{ 3 } }=\frac { 7! }{ (7-3)!*3! } *\frac { 6! }{ (6-3)!*3! }

= \frac { 7! }{ 4!*3! } *\frac { 6! }{ 3!*3! }

= 35*20 = 700

Case II : When Mr. Y is not included in the committee :

Then , we need to select 3 ladies from 8 ladies and 4 gentlemen from 6 gentlemen as Y is not included.

No of ways = { 8 }_{ { C }_{ 3 } }*{ 6 }_{ { C }_{ 4 } }=\frac { 8! }{ (8-3)!*3! } *\frac { 6! }{ (6-4)!*4! }

= 56 * 15 = 840

Hence, total number of ways = 700 + 840 = 1540

Hence , OPTION(c)


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