## Permutation and Combination problems

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

• Options
• A. 120
• B. 720
• C. 4320
• D. 2160
• E. None of these
• 2. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

• Options
• A. 32
• B. 48
• C. 64
• D. 96
• E. None of these
• 3. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

• Options
• A. 210
• B. 1050
• C. 25200
• D. 21400
• E. None of these
• 4. In how many ways can the letters of the word 'LEADER' be arranged?

• Options
• A. 72
• B. 144
• C. 360
• D. 720
• E. None of these
• 5. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

• Options
• A. 32
• B. 48
• C. 36
• D. 60
• E. 120
• 6. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

• Options
• A. 360
• B. 480
• C. 720
• D. 5040
• E. None of these
• 7. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

• Options
• A. 266
• B. 5040
• C. 11760
• D. 86400
• E. None of these
• 8. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

• Options
• A. 810
• B. 1440
• C. 2880
• D. 50400
• E. 5760
• 9. 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?

• Options
• A. 5
• B. 10
• C. 15
• D. 20
• 10. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

• Options
• A. 63
• B. 90
• C. 126
• D. 45
• E. 135