How many organizational structures can be formed that consist of Divis

Question

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

push12345 · Accepted Answer

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

KarishmaB · Answer

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

ParthSanghavi · Answer

Understood. Thanks for a quick response  VeritasKarishma

chetan2u · Answer

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

chetan2u · Answer

Seems, Karishma has also replied in the meantime. Thanks

ccheryn · Answer

hi experts,

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

thanks

JeremyLee95 · Answer

One also does not quote simply C1/C2 to make a problem more complex.

PituxaBR · Answer

I have the same question ....

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How many organizational structures can be formed that consist of Divis

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How many organizational structures can be formed that consist of Divis

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