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Saumyojit

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From 4 gentleman and 4 ladies a committee of 5 is to be formed which consist of a president,vice-president and three secretaries.

What will be the number of ways of selecting the committee with a maximum of 2 women and having at the maximum one woman holding one of the two posts( president,vice-president ) in the committee.




CASE 1: one lady &4 gent : 4c1 —> selecting one lady
4c4 —-> selecting 4 gents out of four

Arrangement : Presid Vp S S S —> no of ways :
Dividing by 3! as rearrangement btwn secretary position is useless
( 4c1 * 4c4 * 5! ) / 3! = 480/6= 80

CASE 2
Two lady & 3 gent (one lady will be in either vp or p )
: In this case we have to make sure that ATMOST one lady can sit in any one of two posts (vp , p)

4c1*2 —> Selecting one lady out of 4 then Lady 1 is selected she has either Vp or p position to select .

Then selecting one out of 4 gent so that it occupies remaining one of vp ,p posts —> 4c1 * 1c1


Rest two gents will have 2 post out of three positions And one lady will take the remaining post .

4 + 8 =12

CAse 3: Two lady and three gent ( lady is not sitting in vp or p post )

Selecting two gent to occupy p and Vp posts : 4c2 *2

Selecting two ladies out of 4 : 4c2

one gent is selected and placed in the reamaining position .

No of ways = 6 *2 * 6 = 72

72 + 12 + 80 = 162

Where am i wrong?
 
Saumyojit said:
CASE 2
Two lady & 3 gent (one lady will be in either vp or p )
: In this case we have to make sure that ATMOST one lady can sit in any one of two posts (vp , p)

4c1*2 —> Selecting one lady out of 4 then Lady 1 is selected she has either Vp or p position to select .

Then selecting one out of 4 gent so that it occupies remaining one of vp ,p posts —> 4c1 * 1c1


Rest two gents will have 2 post out of three positions And one lady will take the remaining post .

4 + 8 =12
Click to expand...
Why did you add?
 
Dr.Peterson said:
That's not true of the sum I asked about, only the one at the end. Please expand the quoted part to see what I referred to: 4+8=12.
Click to expand...
yes 32 it will be.
4*8=32 .
My concentration is low .
ansqwer is 512
 
Last edited:
Saumyojit said:
yes 32 it will be.
4*8=32 .
My concentration is low .
ansqwer is 512
Click to expand...
Are you sure those are the right numbers to multiply? Please explain your reasoning again, now that you are thinking a little more clearly.
 
Saumyojit said:
CASE 1: one lady &4 gent : 4c1 —> selecting one lady
4c4 —-> selecting 4 gents out of four

Arrangement : Presid Vp S S S —> no of ways :
Dividing by 3! as rearrangement btwn secretary position is useless
( 4c1 * 4c4 * 5! ) / 3! = 480/6= 80

CASE 2
Two lady & 3 gent (one lady will be in either vp or p )
: In this case we have to make sure that ATMOST one lady can sit in any one of two posts (vp , p)

4c1*2 —> Selecting one lady out of 4 then Lady 1 is selected she has either Vp or p position to select .

Then selecting one out of 4 gent so that it occupies remaining one of vp ,p posts —> 4c1 * 1c1


Rest two gents will have 2 post out of three positions And one lady will take the remaining post .

4 * 8 =32

CAse 3: Two lady and three gent ( lady is not sitting in vp or p post )

Selecting two gent to occupy p and Vp posts : 4c2 *2

Selecting two ladies out of 4 : 4c2

one gent is selected and placed in the reamaining position .
Click to expand...
this is my reasoning . I have the same explanation .

Three cases .
 
We're looking at just this one case that I questioned:
Saumyojit said:
CASE 2
Two lady & 3 gent (one lady will be in either vp or p )
: In this case we have to make sure that ATMOST one lady can sit in any one of two posts (vp , p)

4c1*2 —> Selecting one lady out of 4 then Lady 1 is selected she has either Vp or p position to select .

Then selecting one out of 4 gent so that it occupies remaining one of vp ,p posts —> 4c1 * 1c1


Rest two gents will have 2 post out of three positions And one lady will take the remaining post .

4 * 8 =32
Click to expand...
I suggested that you should think about changing something other than that last line. Have you done so?

Putting it together, you have

4c1 * 2 * 4c1 * 1c1​
Select one of 4 ladies; select one of 2 positions for her; select one of 4 gents for the other position (and select that position in 1 way).​

But don't you have to select people to be secretaries? So far you have only placed two people on the committee.

Here was the problem:
Saumyojit said:
From 4 gentleman and 4 ladies a committee of 5 is to be formed which consist of a president,vice-president and three secretaries.

What will be the number of ways of selecting the committee with a maximum of 2 women and having at the maximum one woman holding one of the two posts( president,vice-president ) in the committee.
Click to expand...
The case under consideration requires "Two ladies & 3 gents (one lady will be in either vp or p)", so you have to choose a lady and 2 gents for the committee.
 
case 1 : 80
case 2 : 4c1 *2 * 4c1 * 3c2 *3c1 --> 288
case 3 : 4c2 *2 * 4c2 * 2c1--> 144
512 answer
YOu were right sir
I have a big lack of concentration although my approach was right .
 
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