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- Question
If a+b+c =21 what is the total number of positive integral solutions?
Options- A. 109
- B. 190
- C. 901
- D. 910
- Correct Answer
- 190
ExplanationNumber of positive integral solutions = = = 190
- 1. 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
- 2. 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
- 3. 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
- 4. In how many ways can 5 letters be posted in 4 letter boxes?
Options- A. 512
- B. 1024
- C. 625
- D. 20 Discuss
- 5. 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
- 6. 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
- 7. In how many different ways could couples be picked from 6 men and 9 women ?
Options- A. 26
- B. 54
- C. 52
- D. 28 Discuss
- 8. The number of sequences in which 4 players can sing a song, so that the youngest player may not be the last is ?
Options- A. 2580
- B. 3687
- C. 4320
- D. 5460 Discuss
- 9. In how many ways the word 'SCOOTY' can be arranged such that 'S' and 'Y' are always at two ends?
Options- A. 720
- B. 360
- C. 120
- D. 24 Discuss
- 10. A box contains 2 blue balls, 3 green balls and 4 yellow balls. In how many ways can 3 balls be drawn from the box, if at least one green ball is to be included in the draw?
Options- A. 48
- B. 24
- C. 64
- D. 32 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 729
Explanation:
Choose 5 starters from a team of 12 players. Order is not important.
= 729
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: 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: 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: 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: 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.
Correct Answer: 54
Explanation:
Number of mens = 8
Number of womens = 5
Different ways could couples be picked = = 9 x 6 = 54 ways.
Correct Answer: 4320
Explanation:
Let 'Y' be the youngest player.
The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.
The required number of ways = 3(3!) = 4320.
Correct Answer: 24
Explanation:
Given word is SCOOTY
ATQ,
Except S & Y number of letters are 4(C 2O's T)
Hence, required number of arrangements = 4!/2! x 2! = 4!
= 4 x 3 x 2
= 24 ways.
Correct Answer: 64
Explanation:
Total number of balls = 2 + 3 + 4 = 9
Total number of ways 3 balls can be drawn from 9 = 9C3
No green ball is drawn = 9 - 3 = 6 = 6C3
Required number of ways if atleast one green ball is to be included = Total number of ways - No green ball is drawn
= 9C3 - 6C3
= 9x8x7/3x2 - 6x5x4/3x2
= 84 - 20
= 64 ways.
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