Of the twelve participants in a certain competition

Question

Of the twelve participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?

3
4
6
9
20

OE

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M: 12 x ½ = 6
M (Under 18yr) = 6 x ½ = 3
F: 6
F (Under 18yr) = 6 x ½ = 3 → F (Over 18yr) = 3
3C2 x 3C2 = 3 x 3 = 9

A. 3
B. 4
C. 6
D. 9
E. 20

OE
 M: 12 x ½ = 6
M (Under 18yr) = 6 x ½ = 3
F: 6
F (Under 18yr) = 6 x ½ = 3 → F (Over 18yr) = 3
3C2 x 3C2 = 3 x 3 = 9

mikemcgarry · Accepted Answer

Dear goodyear2013 , I'm happy to respond. :-)

I suppose it's not clear to me whether you have a question and, if so, what it is. Of 12 participants, half (6) are males, and of these 6 males, half (3) are younger than 18. Thus, so far, we have 3 males younger than 18 3 males older than 18 Now, there must be 12 - 6 = 6 females. Of these 6 females, half (3) are younger than 18. Thus, we have 3 females younger than 18 3 females older than 18 Now, for the 4 competitor collection, we need two of the three males younger than 18, and two of the three females older than 18. That's 3C2 = 3 choices for the two males, and 3C2 = 3 choices for the females. Apply the Fundamental Counting Principle, explained in this post: https://magoosh.com/gmat/2012/gmat-quant-how-to-count/ 3*3 = 9 possible four-competitor collections. Does all this make sense? Mike :-)

JusTLucK04 · Answer

M under 18 - 3 
F above 18 - 3

How many distinct groups can be formed now: 3c2 * 3c2 = 9

sshrivats · Answer

total 12 participants

half are male --> 6 males
half the males are under 18 --> 3 males under 18

same for females --> 3 females above 18

groups of four ( out of which 2 are males below 18 and 2 are females above 18) = 3C2 * 3C2 = 3*3 =9

bumpbot · Answer

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Of the twelve participants in a certain competition

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