4.Amit has five friends: 3 girls and 2 boys. Amit's wife also has 5 friends : 3 boys and 2
girls. In how many maximum number of different ways can they invite 2 boys and 2 girls such
that two of them are Amit's friends and two are his wife's? [spoiler](Ans:c)[/spoiler]
(a) 24
(b) 38
(c) 46
(d) 58
(e)68
Counting
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Hi Arun6765,
In the future, you should make sure to post questions into the proper subForums. For example, the PS Forum is here:
https://www.beatthegmat.com/problemsolvingf6.html
This specific type of prompt is relatively rare (you probably won't see it on Test Day). From a 'math standpoint', you can solve it by using the Combination Formula in a really specific way:
The question asks for the number of 'groups' that can be formed of 2 boys and 2 girls (with the added condition that 2 people come from Amit's friends and 2 come from his wife's friends). There are 3 ways that this can occur....
1) 2 boys from Amit; 2 girls from his wife
2) 2 girls from Amit; 2 boys from his wife
3) 1 boy and 1 girl from each
1st option = (2C2)(2C2) = (1)(1) = 1 option
2nd option = (3C2)(3C2) = (3)(3) = 9 options
3rd option = (3)(2)(3)(2) = 36 options
Total = 1+9+36 = 46
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
In the future, you should make sure to post questions into the proper subForums. For example, the PS Forum is here:
https://www.beatthegmat.com/problemsolvingf6.html
This specific type of prompt is relatively rare (you probably won't see it on Test Day). From a 'math standpoint', you can solve it by using the Combination Formula in a really specific way:
The question asks for the number of 'groups' that can be formed of 2 boys and 2 girls (with the added condition that 2 people come from Amit's friends and 2 come from his wife's friends). There are 3 ways that this can occur....
1) 2 boys from Amit; 2 girls from his wife
2) 2 girls from Amit; 2 boys from his wife
3) 1 boy and 1 girl from each
1st option = (2C2)(2C2) = (1)(1) = 1 option
2nd option = (3C2)(3C2) = (3)(3) = 9 options
3rd option = (3)(2)(3)(2) = 36 options
Total = 1+9+36 = 46
Final Answer: C
GMAT assassins aren't born, they're made,
Rich

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Such an original quastion! Why do I have to think about maximum number of different ways to invite the friends? Is it so important?))Arun6765 wrote:4.Amit has five friends: 3 girls and 2 boys. Amit's wife also has 5 friends : 3 boys and 2
girls. In how many maximum number of different ways can they invite 2 boys and 2 girls such
that two of them are Amit's friends and two are his wife's? [spoiler](Ans:c)[/spoiler]
(a) 24
(b) 38
(c) 46
(d) 58
(e)68

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 Location: East Bay all the way
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A quaint one too  who gets invited to anything any more? It seems like people just digitally announce events (or maybe I've been living in California too long ...)AlexBarret wrote:Such an original quastion! Why do I have to think about maximum number of different ways to invite the friends? Is it so important?))Arun6765 wrote:4.Amit has five friends: 3 girls and 2 boys. Amit's wife also has 5 friends : 3 boys and 2
girls. In how many maximum number of different ways can they invite 2 boys and 2 girls such
that two of them are Amit's friends and two are his wife's? [spoiler](Ans:c)[/spoiler]
(a) 24
(b) 38
(c) 46
(d) 58
(e)68