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- Question
In how many different ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together?
Options- A. 1440
- B. 720
- C. 2250
- D. 3600
- Correct Answer
- 3600
ExplanationGiven word is THERAPY.
Number of letters in the given word = 7
These 7 letters can be arranged in 7! ways.
Number of vowels in the given word = 2 (E, A)
The number of ways of arrangement in which vowels come together is 6! x 2! ways
Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.
- 1. If repetition of the digits is allowed, then the number of even natural numbers having three digits is :
Options- A. 550
- B. 450
- C. 500
- D. 540 Discuss
- 2. Compute the sum of 4 digit numbers which can be formed with the four digits 1,3,5,7, if each digit is used only once in each arrangement.
Options- A. 105555
- B. 106665
- C. 106656
- D. 108333 Discuss
- 3. 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
- 4. 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
- 5. 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
- 6. In how many ways the letters of the word NUMERICAL can be arranged so that the consonants always occupy the even places ?
Options- A. 5!
- B. 6!
- C. 4!
- D. Can't determine Discuss
- 7. 5 men and 4 women are to be seated in a row so that the women occupy the even places . How many such arrangements are possible?
Options- A. 2880
- B. 1440
- C. 720
- D. 2020 Discuss
- 8. In how many ways can 5 letters be posted in 4 letter boxes?
Options- A. 512
- B. 1024
- C. 625
- D. 20 Discuss
- 9. Using numbers from 0 to 9 the number of 5 digit telephone numbers that can be formed is
Options- A. 1,00,000
- B. 59,049
- C. 3439
- D. 6561 Discuss
- 10. If you have 6 New Year greeting cards and you want to send them to 4 of your friends, in how many ways can this be done?
Options- A. 720
- B. 360
- C. 240
- D. 740 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 450
Explanation:
In a 3 digit number one?s place can be filled in 5 different ways with (0,2,4,6,8)
10?s place can be filled in 10 different ways
100?s place can be filled in 9 different ways
There fore total number of ways = 5X10X9 = 450
Correct Answer: 106656
Explanation:
The number of arrangements of 4 different digits taken 4 at a time is given by = 4! = 24.All the four digits will occur equal number of times at each of the position,namely ones,tens,hundreds,thousands.
Thus,each digit will occur 24/4 = 6 times in each of the position.The sum of digits in one's position will be 6 x (1+3+5+7) = 96.Similar is the case in ten's,hundred's and thousand's places.
Therefore,the sum will be 96 + 96 x 10 + 96 x 100 + 96 x 100 = 106656
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
Correct Answer: F is second to the right of B
Correct Answer: 2
Correct Answer: Can't determine
Explanation:
NUMERICAL has 9 positions in which 2, 4, 6, 8 are even positions.
And it contains 5 consonents i.e, N, M, R, C & L. Hence this cannot be done as 5 letters cannot be placed in 4 positions.
Therefore, Can't be determined.
Correct Answer: 2880
Explanation:
There are total 9 places out of which 4 are even and rest 5 places are odd.
4 women can be arranged at 4 even places in 4! ways.
and 5 men can be placed in remaining 5 places in 5! ways.
Hence, the required number of permutations = 4! x 5! = 24 x 120 = 2880
Correct Answer: 1024
Explanation:
First letter can be posted in 4 letter boxes in 4 ways. Similarly second letter can be posted in 4 letter boxes in 4 ways and so on.
Hence all the 5 letters can be posted in = 4 x 4 x 4 x 4 x 4 = 1024
Correct Answer: 3439
Explanation:
The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.
This can be done in ways, but '0' is there
So, the numbers starting with '0' are to be excluded is numbers.
Total 5 digit telephone numbers = = 3439
Correct Answer: 360
Explanation:
We have to find number of permutations of 4 objects out of 6 objects.
This number is = 360
Therefore, cards can be sent in 360 ways.
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