How many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women pick one option?

Correct Answer:

Description for Correct answer:

There are 7 men and 3 women. We have to select 5 men out of 7 and 2 women out of 3. This can be done in \( \Large ^{7}C_{5} \times ^{3}C_{2} \) ways. The number of ways of making the selection = \( \Large ^{7}C_{5} \times ^{3}C_{2} \)= \( \Large ^{7}C_{2} \times ^{3}C_{2} \)\( \Large \left[ Because,\ ^{n}C_{r}=^{n}C_{n-r} \right] \)

= \( \Large \frac{7 \times 6}{1 \times 2} \times \frac{3 \times 2}{1 \times 2} \) = 63

Part of solved Permutation and combination questions and answers : >> Aptitude >> Permutation and combination

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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.

Page 2

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.

If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.

Answer & Explanation Answer: D) R

Explanation:

The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.

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In how many ways can a group of 5 men and 2 women be made out of total of 7 men and 3 women?

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