How many ways can a group of 7 members be formed from 6 boys and 5 girls if the group must have 4 boys?

Exercise :: Permutation and Combination - General Questions

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

Answer: Option D

Explanation:

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20.

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Exercise :: Permutation and Combination - General Questions

13.

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

A.	10080
B.	4989600
C.	120960
D.	None of these

Answer: Option C

Explanation:

In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.

Thus, we have MTHMTCS (AEAI).

Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters =	8!	= 10080.
(2!)(2!)

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters =	4!	= 12.
2!

Required number of words = (10080 x 12) = 120960.

1) 120

2) 80

3) 90

4) 100

Answer: (4) 100

Solution: Given, there are 6 boys and 4 girls.

We need to form a group of 7 with these boys and girls, with the majority of boys present in it.

Therefore, it can be done in 6C4 x 4C3 x 6C5 x 4C2 x 6C6 x 4C1 ways.

Thus, the answer is 100

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How many ways can a group of 7 members be formed from 6 boys and 5 girls if the group must have 4 boys?

Exercise :: Permutation and Combination - General Questions

Page 2

Exercise :: Permutation and Combination - General Questions

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