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- Question
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
- Correct Answer
- 325
ExplanationRequired number of signals =
= 5 + 20 + 60 + 120 + 120 = 325
- 1. 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
- 2. 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
- 3. 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
- 4. 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 Discuss
- 5. 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
- 6. 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
- 7. There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?
Options- A. 1000
- B. 625
- C. 525
- D. 125 Discuss
- 8. Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?
Options- A. 28
- B. 56
- C. 44
- D. 36 Discuss
- 9. How many three digit numbers 'abc' are formed where two of the three digits are same ?
Options- A. 252
- B. 648
- C. 243
- D. 900 Discuss
- 10. The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
Options- A. 2(6!)
- B. 6! x 7
- C. 6! x ?P?
- D. None Discuss
Permutation and Combination problems
Search Results
Correct Answer: 253
Explanation:
Number of non - negative integral solutions = = 253
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: 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: 720
Explanation:
There 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
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: 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.
Correct Answer: 125
Explanation:
Methods for selecting 4 questions out of 5 in the first section = 5 x 4 x 3 x 2 x 1/4 x 3 x 2 x 1 = 5. Similarly for other 2 sections also i.e 5 and 5
So total methods = 5 x 5 x 5 = 125.
Correct Answer: 36
Explanation:
Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by ways i.e children.
Number of children= = 9 x 8 / 1x 2 = 36.
Correct Answer: 243
Explanation:
Digits are 0,1,2,3,4,5,6,7,8,9. So no. of digits are 10
First all possible case => 9(0 excluded) x 10 x 10 = 900
Second no repetition allowed =>9 x 9 x 8 = 648
Third all digits are same => 9 (111,222,333,444,555,666,777,888,999)
Three digit numbers where two of the three digits are same = 900 - 648 - 9 = 243 ;
Correct Answer: 6! x ?P?
Explanation:
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ?P? ways.
Hence required number of ways = 6! x ?P?
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