Permutation and Combination with Explanation

Q1. How many words can be formed with the letters of the word MUKESH such that every word begins with a vowel and ends with a vowel?

A. 50 B. 48
C. 52 D. 65

Q2. Six persons enter a railway compartment in which there are nine seats. In how many ways they take their places? If there are only seven seats for them, is there any change in the number of arrangements?

A. 60480, 5040 B. 45802, 4510
C. 87452, 9658 D. 32457, 6542

Q3. Calculate permutations of the letters of the following word SOFTWARE?

A. 32040 B. 52148
C. 42320 D. 40320

Q4. In how many ways the word ARTICLE may be arranged, when the vowels are evenly placed in the word.

A. 145 B. 120
C. 144 D. 140

Q5. In how many ways the word MANAGEMENT can be made out of the letters of the word?

A. 2245700 B. 226800
C. 228680 D. 224567

Q6. In how many ways three Americans, three Indians, and three Japanese may sit around a round table in such a way that persons of the same nationality sit together?

A. 432 B. 430
C. 445 D. 444

Q7. In how many ways a cricket eleven may be selected out of 15 players, if (i) one specific player is to be selected in the team; (ii) one specific player is not to be included in the team.

A. 1000, 650 B. 1002, 365
C. 1003, 380 D. 1001, 364