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Algebra

Blazing goIITian

Joined:	19 Nov 2007
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17 Apr 2008 22:13:52 IST

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555

rates assured permutation

None

from a panel of 5 lawyers , 5 chartered accountant and 1 lawyer who is also an charyered accountant ,how many committees of 4 can be made if each comimittee is to contain at least 1 lawyer and 1 chartered accoumtant

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varun kinhal

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Joined: 22 Feb 2007

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17 Apr 2008 22:31:19 IST

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is it 11c4/2*5c4;
i m not sure abt ans.

SHAILESH

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17 Apr 2008 22:35:35 IST

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ans = 320

varun kinhal

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17 Apr 2008 22:37:26 IST

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oops

Akhil

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17 Apr 2008 22:37:49 IST

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let 5 lawyers=A
5 CAs=B
1 lawyer/CA=C

to choose 4
possibilites are
3A 1B + 1A 3B= 2* 5C3*5C1=2*10*5=100
2A 2 B= 5C2*5C2=10*10=100

3A1C/3B 1 C= 2x5C3=20
2A 1B 1 C/2B 1A 1 C=2x5C2x5C1=100

so adding all these cases
320 possibilities

Priyesh

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17 Apr 2008 22:57:54 IST

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case 1 : person who is both lawyer & accountant is selected , then any three from the rest 10 can be selected

so no .of ways = 10C3 = 120

case 2: the uniquely talented above person is not selected leaving three possibilites

i) 2 lawyers & 2 accountants are selected , no .of ways = 5C2 * 5C2 = 100

ii) (3 lawyers and 1 accountant) or (1 lawyer & 3 accountants) = 2*5C3*5C1 = 100

so total ways = 120 + 200 = 320

$^Mujtaba^$

Blazing goIITian

Joined: 15 Nov 2007

Posts: 436

17 Apr 2008 23:02:36 IST

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See this tabular form i have adopted to show this:

	No. of selections that can be made
5 Lawyers	3	2	1	2	1	3	0

3 CA's	1	2	3	1	2	0	3

1 lawyer/CA	0	0	0	1	1	1	1

This states that in how many ways 4 people can be selected from the given people.

If u add all the 7 cases above u will surely get 320.

$^Mujtaba^$

Blazing goIITian

Joined: 15 Nov 2007

Posts: 436

17 Apr 2008 23:10:37 IST

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See the working now, if u didn't get.

(5C3 x 5C1) + (5C2 x 5C2) + (5C1 x 5C3) + (5C2 x 5C1) + (5C1 x 5C2) + (5C3 + 5C3)=
50 + 100 + 50 + 50 + 50 + 10 + 10 =320

I haven't shown 5C0 and 1C1 in the working.
I hope its useful and understandable.

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