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- Question
How many arrangements of the letters of the word ?BENGALI? can be made if the vowels are never together.
Options- A. 120
- B. 640
- C. 720
- D. 540
- Correct Answer
- 720
ExplanationThere are 7 letters in the word ?Bengali of these 3 are vowels and 4 consonants.
Considering vowels a, e, i as one letter, we can arrange 4+1 letters in 5! ways in each of which vowels are together. These 3 vowels can be arranged among themselves in 3! ways.
Total number of words = 5! x 3!= 120 x 6 = 720
- 1. In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together?
Options- A. 360
- B. 720
- C. 120
- D. 840 Discuss
- 2. If A1, A2, A3, A4, ..... A10 are speakers for a meeting and A1 always speaks after, A2 then the number of ways they can speak in the meeting is
Options- A. 9!
- B. 9!/2
- C. 10!
- D. 10!/2 Discuss
- 3. Out of 6 green ball, 4 blue ball, in how many ways we selectone or more balls ?
Options- A. 42
- B. 34
- C. 31
- D. 22 Discuss
- 4. A box contains 2 blue balls, 3 green balls and 4 yellow balls. In how many ways can 3 balls be drawn from the box, if at least one green ball is to be included in the draw?
Options- A. 48
- B. 24
- C. 64
- D. 32 Discuss
- 5. In how many ways the word 'SCOOTY' can be arranged such that 'S' and 'Y' are always at two ends?
Options- A. 720
- B. 360
- C. 120
- D. 24 Discuss
- 6. There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf ?
Options- A. 26100
- B. 21600
- C. 24000
- D. 36000 Discuss
- 7. How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?
Options- A. 129780
- B. 1587600
- C. 35600
- D. None of these Discuss
- 8. If a+b+c = 21, what is the total number of non - negative integral solutions?
Options- A. 123
- B. 253
- C. 321
- D. 231 Discuss
- 9. The number of signals that can be generated by using 5 differently coloured flags, when any number of them may be hoisted at a time is:
Options- A. 235
- B. 253
- C. 325
- D. None of these Discuss
- 10. A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?
Options- A. 142
- B. 175
- C. 212
- D. 253 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 360
Explanation:
CAPITAL = 7
Vowels = 3 (A, I, A)
Consonants = (C, P, T, L)
5 letters which can be arranged in
Vowels A,I =
No.of arrangements = 5! x =360
Correct Answer: 10!/2
Explanation:
As A1 speaks always after A2, they can speak only in 1st to 9th places and
A2 can speak in 2nd to 10 the places only when A1 speaks in 1st place
A2 can speak in 9 places the remaining
A3, A4, A5,...A10 has no restriction. So, they can speak in 9.8! ways. i.e
when A2 speaks in the first place, the number of ways they can speak is 9.8!.
When A2 speaks in second place, the number of ways they can speak is 8.8!.
When A2 speaks in third place, the number of ways they can speak is 7.8!. When A2 speaks in the ninth place, the number of ways they can speak is 1.8!
Therefore,Total Number of ways they can speak = (9+8+7+6+5+4+3+2+1) 8! = = 10!/2
Correct Answer: 34
Explanation:
7 × 5 = 35
35 ? 1 = 34
Correct Answer: 64
Explanation:
Total number of balls = 2 + 3 + 4 = 9
Total number of ways 3 balls can be drawn from 9 = 9C3
No green ball is drawn = 9 - 3 = 6 = 6C3
Required number of ways if atleast one green ball is to be included = Total number of ways - No green ball is drawn
= 9C3 - 6C3
= 9x8x7/3x2 - 6x5x4/3x2
= 84 - 20
= 64 ways.
Correct Answer: 24
Explanation:
Given word is SCOOTY
ATQ,
Except S & Y number of letters are 4(C 2O's T)
Hence, required number of arrangements = 4!/2! x 2! = 4!
= 4 x 3 x 2
= 24 ways.
Correct Answer: 21600
Explanation:
4 novels can be selected out of 5 in
ways.
2 biographies can be selected out of 4 in
ways.
Number of ways of arranging novels and biographies =
= 30
After selecting any 6 books (4 novels and 2 biographies) in one of the 30 ways, they can be arranged on the shelf in 6! = 720 ways.
By the Counting Principle, the total number of arrangements = 30 x 720 = 21600
Correct Answer: 1587600
Explanation:
H L C N T A U I O
L N A I
There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.
If all the consonants are together then the numberof arrangements = x 1/2! .
But the 7 consonants can be arranged themselves in x 1/2! ways.
Hence the required number of ways = = 1587600
Correct Answer: 253
Explanation:
Number of non - negative integral solutions = = 253
Correct Answer: 325
Explanation:
Required number of signals =
= 5 + 20 + 60 + 120 + 120 = 325
Correct Answer: 253
Explanation:
The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.
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