If 3 members are to be selected from a team of x members then what is

Question

If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.

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chetan2u · Accepted Answer

If 3 members are to be selected from a group of x members then what is the value of x?

1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
Selecting 3 members from x =xC3
Selecting 3 when the 2 specific members are together=(x-2)C1... 2 selected from x, the remaining 1 can be selected from remaining x-2.
So cases when the 2 are not together=xC3-(x-2)C1=30...
 \frac{x(x-1)(x-2)}{6}-(x-2)=30.....(x-2)(x^2-x-6)=180.......(x-2)(x-3)(x+2)=180=4*5*9 
So x-2=5..x=7
Sufficient

2) There are a total of 35 ways to make team of 3 members out of team of x members.
xC3=35...
 \frac{x(x-1)(x-2)}{6}=35......x(x-2)(x-1)=5*6*7 
x=7
Sufficient

D

kunalcvrce · Answer

we have to find x.

From1 : 2 specific members never being together=Total number of combinations- 2 specific members being together.
Total number of combinations=xC3
 2 specific members being together=(x-1)C3
xC3-(x-1)C3=30

Since one equation one variable . So 1 is sufficient.

From2 : xC3=35

Again one equation one variable . So 2 is also sufficient.

No need to find value it will take your time.

So D.

truongvu31 · Answer

Isnt xC3-(x-1)C3=15??

7C3= 35 and 6C3 =20, or am I wrong?

amanvermagmat · Answer

Actually, it shouldnt be (x-1)C3.. The no of ways of selecting 3 out of x, so that two specific members are together on the team = (x-2)C1.. this is because if we have already fixed two members, then we have to select remaining 1 more member out of (x-2).

So it should be xC3 - (x-1)C2 = 30
And you can check: 7C3 - 5C1 = 35-5 = 30

AliciaSierra · Answer

Bunuel ,

Is (x-2)C1 correct in chetan2u answer ?

GmatPoint · Answer

The total way of selecting a team of r members out of n members is nCr.
Thus, the total ways of selecting a team of 3 members out of x members will be xC3.

1. If the team of 3 members is selected from the group of x members, then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team.

Total ways of selecting 3 members from the group of x members with 2 specific members never being together on the team = (Total ways of selecting 3 members from the group of x members) - (Total ways of selecting 3 members from the group of x members with 2 specific members always being together on the team)

Total ways of selecting 3 members from the group of x members = xC3

Total ways of selecting 3 members from the group of x members with 2 specific members always being together on the team = x (since only one member is left to pick)

Thus, 30 = xC3 - x = (x)(x-1)(x-2)/6 
 30 x 6 = x(x-1)(x-2) 
Or x = 7
Thus, this is sufficient.

2. There are a total of 35 ways to make a team of 3 members out of the team of x members.

Total ways of selecting 3 members from the group of x members = xC3

Thus, 35 = xC3
 35 = x(x-1)(x-2)
 Or, x = 7
Thus, this is sufficient.

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If 3 members are to be selected from a team of x members then what is

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