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- Question
In how many ways can 5 letters be posted in 4 letter boxes?
Options- A. 512
- B. 1024
- C. 625
- D. 20
- Correct Answer
- 1024
ExplanationFirst 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
- 1. 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
- 2. 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
- 3. 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 Discuss
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ?
Options- A. 569
- B. 729
- C. 625
- D. 769 Discuss
- 9. If a+b+c =21 what is the total number of positive integral solutions?
Options- A. 109
- B. 190
- C. 901
- D. 910 Discuss
- 10. If two cards are taken one after another without replacing from a pack of 52 cards. What is the probability for the two cards be Ace ?
Options- A. 51/1221
- B. 42/221
- C. 1/221
- D. 52/1245 Discuss
Permutation and Combination problems
Search Results
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: 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: 3600
Explanation:
Given 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.
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: 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.
Correct Answer: 729
Explanation:
Choose 5 starters from a team of 12 players. Order is not important.
= 729
Correct Answer: 190
Explanation:
Number of positive integral solutions = = = 190
Correct Answer: 1/221
Explanation:
Total Combination of getting a card from 52 cards =
Because there is no replacement, so number of cards after getting first card= 51
Now, Combination of getting an another card=
Total combination of getting 2 cards from 52 cards without replacement= (
)
There are total 4 Ace in stack. Combination of getting 1 Ace is =
Because there is no replacement, So number of cards after getting first Ace = 3
Combination of getting an another Ace =
Total Combination of getting 2 Ace without replacement=
Now,Probability of getting 2 cards which are Ace = = 1/221.
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