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- Question
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there ?
Options- A. 205
- B. 194
- C. 209
- D. 159
- Correct Answer
- 209
ExplanationWe may have (1 boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or(4 boys).
Required number of ways = ( ) + + ( ) + ( )= (24+90+80+15)
= 209.
- 1. In a bag, there are 8 red, 7 blue and 6 green flowers. One of the flower is picked up randomly. What is the probability that it is neither red nor green ? A) 13 B)821 C)621 D)2021
Options- A. Option A
- B. Option B
- C. Option C
- D. Option D Discuss
- 2. In how many ways can letter of the word RAILINGS arrange so that R and S always come together?
Options- A. 1260
- B. 2520
- C. 5040
- D. 1080 Discuss
- 3. The letters of the word PROMISE are to be arranged so that three vowels should not come together. Find the number of ways of arrangements?
Options- A. 4320
- B. 4694
- C. 4957
- D. 4871 Discuss
- 4. In how many different ways can the letters of the word 'HAPPYHOLI' be arranged?
Options- A. 89,972
- B. 90,720
- C. 72,000
- D. 81,000 Discuss
- 5. From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?
Options- A. 91
- B. 104
- C. 109
- D. 98 Discuss
- 6. In how many different ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together?
Options- A. 112420
- B. 85120
- C. 40320
- D. 1209600 Discuss
- 7. What is the value of 100P2 ?
Options- A. 10000
- B. 9900
- C. 8900
- D. 7900 Discuss
- 8. How many such pair of letters are there in the word ?TROUBLED? which have as many letters between them in the word as they have between them in the English alphabet?
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
- 9. A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours. Which of the following is/are correct ?
Options- A. F is third to the left of B
- B. F is second to the right of B
- C. B is an immediate neighbour of D
- D. All of the above Discuss
- 10. Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?
Options- A. 360
- B. 780
- C. 720
- D. 240 Discuss
Permutation and Combination problems
Search Results
Correct Answer: Option A
Explanation:
Total number of flowers = (8+7+6) = 21.
Let E = event that the flower drawn is neither red nor green.
= event taht the flower drawn is blue.
--> n(E)= 7
--> P(E)= =
Correct Answer: 5040
Explanation:
The number of ways in which the letters of the word RAILINGS can be arranged such that R & S always come together is
Count R & S as only 1 space or letter so that RS or SR can be arranged => 7! x 2!
But in the word RAILINGS, I repeated for 2 times => 7! x 2!/2! = 7! ways = 5040 ways.
Correct Answer: 4320
Explanation:
Given Word is PROMISE.
Number of letters in the word PROMISE = 7
Number of ways 7 letters can be arranged = 7! ways
Number of Vowels in word PROMISE = 3 (O, I, E)
Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways
Now, the number of ways of arrangements so that three vowels should not come together
= 7! - (5! x 3!) ways = 5040 - 720 = 4320.
Correct Answer: 90,720
Explanation:
The given word HAPPYHOLI has 9 letters
These 9 letters can e arranged in 9! ways.
But here in the given word letters H & P are repeated twice each
Therefore, Number of ways these 9 letters can be arranged is
Correct Answer: 91
Explanation:
We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
Case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+
=7 ways.
Case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in
=84 ways.
Thus, total number of ways is 7+84= 91 ways.
Correct Answer: 1209600
Explanation:
Given word is TRANSFORMER.
Number of letters in the given word = 11 (3 R's)
Required, number of ways the letters of the word 'TRANSFORMER' can be arranged such that 'N' and 'S' always come together is
10! x 2!/3!
= 3628800 x 2/6
= 1209600
Correct Answer: 9900
Explanation:
Here in 100P2, P says that permutations and is defined as in how many ways 2 objects can be selected from 100 and can be arranged.
That can be done as,
= 100!/(100 - 2)!
= 100 x 99 x 98!/98!
= 100 x 99
= 9900.
Correct Answer: 2
Correct Answer: F is second to the right of B
Correct Answer: 720
Explanation:
We have to arrange 6 books.
The number of permutations of n objects is n! = n. (n ? 1) . (n ? 2) ... 2.1
Here n = 6 and therefore, number of permutations is 6.5.4.3.2.1 = 720
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