Exercise :: Permutation and Combination - General Questions
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13. | In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together? | |||||||||||||||
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.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
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Exercise :: Permutation and Combination - General Questions
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7. | 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. |
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200 Qs. 200 Marks 120 Mins
Formula used:
If we have a group of 'n' objects out of which we make a selection taking 'r' object at a time, then the number of such selections is given by the combination formula
nCr = n!/(r!(n – r!))
Calculation:
Number of groups can be formed by 5 men and 2 women out of 7 men and 3 women
⇒ 7C5 × 3C2
⇒ 7!/(5! × (7 – 5)!) × 3!/(2! × (3 – 2)!)
⇒ 7!/(5! × 2!) × 3!/(2! × 1!)
⇒ (7 × 6 × 5!)/(5! × 2) × (3 × 2!)/(2!)
⇒ (7 × 3) × (3)
⇒ 63
∴ The number of ways to arrange men and women is 63
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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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Similar Questions
Q:
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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