M4maths Previous Puzzles

21 Feb 2019 Combination

There are 31 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender and number of girls and guys in the team should NOT be equal. How many ways can such a team be made?

OPtion

1) 15680
2) 15480
3) 15280
4) 15180
5) 15380
6) 15080
7) 15600
8) 15580
9) 15880
10) None of these

Solution

boys=15 and girls=16 now the combinations are {girl,girl,girl,boy} or {boy,boy,boy,girl}
so 16c3*15c1 + 15c3*16c1 = 560*15 + 455*16 = 15680

Correct Option: 1 Best Solution (6)

G.S.Kantharao   6 years AGO

Girls and Guys are =16,15
Combinations of groups(3g,1gy),(1g,3gy)
No of ways=(16C3 ×15C1)+(16C1 × 15C3)
=8400+7280=15680
Right option is 1👈

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Devendra Marghade   6 years AGO

If number of guys are x then girls are (x+1)
Total students=x+(x+1)=31 or x=15
Therefore, number of guys=15 and girsl=16
So, in a team of 4, as per the given requirements there can be 1 girl & 3 boys OR 3 girls & 1 boy.
Number of ways=16C1 * 15C3 + 16C3 * 15C1=16*455 + 560*15 = 7280 + 8400=15680
Option 1)

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SAYAN CHATTERJEE   6 years AGO

Let, the no of girls be x
So, x+x-1= 31
x= 16, so, no. of boyes is 15
Now, 4 students with the condition hoven can be chosen the ways = 16C3*15C1+15C3*16C1= 15680.
Option 1.

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Varun   6 years AGO

31 guys = 15 boys (b) + 16 girls (g) satisfies the constraint
4 group can be made of :
0 4
1 3
2 2
And we are not supposed to take the combination:
0 4 as it will skew team with single gender
2 2 as it will make equal number of girls and boys


For available combination : 1 3
1 out of 15 b can be taken in 15P1 = 15
And remaining 3 can be taken as 16C3 = 560
=>15*560 = 8400
Similarly if we take for available combination 3 1
=>16*15C3 = 16 * 455 = 7280
=> 8400+7280 = 15680
= Option (1)

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MANISHA JADHAV   6 years AGO

total boys=15 and girls=16
we have to select 1boy and 3girls or 3 boys and 1 girls
way to select =15 16 15 16
C * C + C * C=8400+7280
1 3 3 1

=15680

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RAMADURAI NATESAN   6 years AGO

Let G denote girls and B boys. G+B=31.and G=B+1.
Hence,b=15 and G=16.Based on the conditions, team could be 3B and 1G or 3G and 1 B.Possible combinations are:
15C3 * 16C1 + 15C1*16C3.Solving,we get 15680.

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