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- Question
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
- Correct Answer
- 4320
ExplanationGiven 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.
- 1. 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
- 2. 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
- 3. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
Options- A. 126
- B. 120
- C. 146
- D. 156 Discuss
- 4. How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never beings separated?
Options- A. 1440
- B. 720
- C. 360
- D. 640 Discuss
- 5. 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. 209
- B. 290
- C. 200
- D. 208 Discuss
- 6. 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
- 7. 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
- 8. 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 Discuss
- 9. 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
- 10. What is the value of 100P2 ?
Options- A. 10000
- B. 9900
- C. 8900
- D. 7900 Discuss
Permutation and Combination problems
Search Results
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: 126
Explanation:
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
=56 + 70= 126
Correct Answer: 1440
Explanation:
There are 7 letters in the word DRAUGHT, the two vowels are A and U. Since, the vowels are not to be separated, AU can be considered as one entity. Therefore, the number of letters will be 6 instead of 7. The permutations will be P(6,6) = 6! ways.
But the two vowels A and U can be arranged in two ways, i.e. AU and UA. The required number of arrangements = 2!.6! = 1440 ways.
Correct Answer: 209
Explanation:
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways =
= = 209.
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: 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: 209
Explanation:
We 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.
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.
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