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Re: How many organizational structures can be formed that consist of Divis [#permalink]
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kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132


Hi ParthSanghavi,

The way would be to see how each set will turn out to be..
consist of Division A - 1 way;
at least one of Divisions B and C - there will be one way when none will be there, so Total-1=2^2-1=3;
at least two of Divisions D, E, and F- none is there-1 way and one is there-3 ways, so total-(1+3)=2^3-4; and
at least two of Divisions G, H, J, and K- none is there-1 way and one is there-4 ways, so total-(1+3)=2^4-5;

total ways = \(1*3*(2^3-4)(2^4-5)=1*3*4*11=132\)
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
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push12345 wrote:
For this question one needs to manually calculate cases

1*(2C1+2C2)*(3C2+3C3)*(4C2+4C3+4C4)
=1*3*4*11
=132

Posted from my mobile device


One also does not quote simply C1/C2 to make a problem more complex.
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
VeritasKarishma wrote:
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132


Division A can be taken in 1 way.

Ways of selecting at least one of B and C = 2^2 - 1 = 3
Explanation: B can be picked in 2 ways (pick or not pick) and C can be picked in 2 ways (pick or not pick). This gives us 2*2 = 4 total ways. Out of this, it is not acceptable to not pick either so we remove 1.

Ways of selecting at least two of D, E and F = 2^3 - 1 - 3 = 4
Explanation: D can be picked in 2 ways (pick or not pick), E can be picked in 2 ways (pick or not pick) and F can be picked in 2 ways (pick or not pick). This gives us 2*2*2 = 8 total ways. Out of this, it is not acceptable to not pick any so we remove 1. It is also not acceptable to pick only 1 (since at least 2 have to picked) so remove 3 ways in which you can pick any one.

Ways of selecting at least 2 of G, H, J, K = 2^4 - 1 - 4 = 11
Same explanation as above.

Total = 1*3*4*11 = 132



Understood. Thanks for a quick response VeritasKarishma
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
Expert Reply
chetan2u wrote:
kchen1994 wrote:
How many organizational structures can be formed that consist of Division A; at least one of Divisions B and C; at least two of Divisions D, E, and F; and at least two of Divisions G, H, J, and K?

a) 60
b) 90
c) 99
d) 120
e) 132


Hi ParthSanghavi,

The way would be to see how each set will turn out to be..
consist of Division A - 1 way;
at least one of Divisions B and C - there will be one way when none will be there, so Total-1=2^2-1=3;
at least two of Divisions D, E, and F- none is there-1 way and one is there-3 ways, so total-(1+3)=2^3-4; and
at least two of Divisions G, H, J, and K- none is there-1 way and one is there-4 ways, so total-(1+3)=2^4-5;

total ways = \(1*3*(2^3-4)(2^4-5)=1*3*4*11=132\)


Seems, Karishma has also replied in the meantime. Thanks
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
hi experts,

could anybody help me in explaining the question please, i am struck in understanding the question per se...

thanks
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
ccheryn wrote:
hi experts,

could anybody help me in explaining the question please, i am struck in understanding the question per se...

thanks


I have the same question ....
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
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Re: How many organizational structures can be formed that consist of Divis [#permalink]
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