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23 Feb 2021, 05:30
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C
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Difficulty:
75%
(hard)
Question Stats:
63% (03:22) correct
37%
(03:11)
wrong
based on 121
sessions
History
Date
Time
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Not Attempted Yet
7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife has also 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’s relatives?
A. 470
B. 475
C. 485
D. 490
E. 500
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. 470
B. 475
C. 485
D. 490
E. 500
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
23 Feb 2021, 19:19
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Bunuel
So we have :
.................F.......M
Husband....4.......3
Wife..........3.......4
Ways to choose 3 F and 3 M, while also ensuring 3 from relatives of each.
1) All 3 ladies from Husband's relatives, so all 3 from the wife's relatives will be men.
4C3*4C3=4*4=16
2) 2 ladies and 1 man from Husband's relatives, so 2 men and 1 lady from wife's relatives.
(4C2*3C1)*(4C2*3C1)=6*3*6*3=324
3) 1 lady and 2 men from Husband's relatives, so 1 man and 2 ladies from wife's relatives.
(4C1*3C2)*(4C1*3C2)=4*3*4*3=144
4) All 3 men from Husband's relatives, so all 3 from the wife's relatives will be ladies.
3C3*3C3=1*1=1
Total = 16+324+144+1=385
C
12 Mar 2021, 15:16
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Bunuel
Solution:
We can use the following table to list the number of relatives by gender who can be invited to the dinner party and determine the number of ways each case can be done.
Attachment:
husbandwifechart.png [ 12.41 KiB | Viewed 3127 times ]
Therefore, the total number of ways is 1 + 144 + 324 + 16 = 485.
Answer: C
