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Bunuel
The I Eta Pi fraternity must choose a delegation of 3 senior members and 2 junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

A. 55
B. 70
C. 200
D. 6,050
E. 12,100

total arragements possible
12c3*11c2 ; 12100
IMO E
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Bunuel
The I Eta Pi fraternity must choose a delegation of 3 senior members and 2 junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

A. 55
B. 70
C. 200
D. 6,050
E. 12,100

Total = 11c2*12c3
= (11*10/2!)*(12*11*10/3!)
= (11*10/2)*(12*11*10/6)
= (11*5)*(2*11*10)
= 11^2*10^2
= 121*100
= 12100

IMO Option E

Pls Hit kudos if you like the solution

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Bunuel
The I Eta Pi fraternity must choose a delegation of 3 senior members and 2 junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

A. 55
B. 70
C. 200
D. 6,050
E. 12,100

3 senior members can be selected in 12C3 = (12 x 11 x 10)/3! = 2 x 11 x 10 = 220 ways.

2 junior members can be selected in 11C2 = (11 x10)/2! =55 ways.

Thus, the delegation can be selected in 220 x 55 = 12,100 ways.

Answer: E
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Bunuel
The I Eta Pi fraternity must choose a delegation of 3 senior members and 2 junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

A. 55
B. 70
C. 200
D. 6,050
E. 12,100

3 senior members can be selected in 12C3 = (12 x 11 x 10)/3! = 2 x 11 x 10 = 220 ways.

2 junior members can be selected in 11C2 = (11 x10)/2! =55 ways.

Thus, the delegation can be selected in 220 x 55 = 12,100 ways.

Answer: E

ScottTargetTestPrep

Thank you for this helpful response. To clarify, are you using the combination formula --> C(n,r)= n!/(r!(n-r)!)
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Bunuel
The I Eta Pi fraternity must choose a delegation of 3 senior members and 2 junior members for an annual interfraternity conference. If I Eta Pi has 12 senior members and 11 junior members, how many different delegations are possible?

A. 55
B. 70
C. 200
D. 6,050
E. 12,100

3 senior members can be selected in 12C3 = (12 x 11 x 10)/3! = 2 x 11 x 10 = 220 ways.

2 junior members can be selected in 11C2 = (11 x10)/2! =55 ways.

Thus, the delegation can be selected in 220 x 55 = 12,100 ways.

Answer: E

ScottTargetTestPrep

Thank you for this helpful response. To clarify, are you using the combination formula --> C(n,r)= n!/(r!(n-r)!)

I'm using a version of that formula. We call it the "box and fill method" in TTP.
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ScottTargetTestPrep
Thank you for your response! To clarify, can you use the regular combination formula that I mentioned in this problem/in other problems in this nature going forward?
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ScottTargetTestPrep
Thank you for your response! To clarify, can you use the regular combination formula that I mentioned in this problem/in other problems in this nature going forward?

Yes, you can.
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