Discussion
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- Question
How many 3-digit numbers can be formed with the digits 1,4,7,8 and 9 if the digits are not repeated ?
Options- A. 60
- B. 26
- C. 50
- D. 64
- Correct Answer
- 60
ExplanationThree digit number will have unit?s, ten?s and hundred?s place.
Out of 5 given digits any one can take the unit?s place.
This can be done in 5 ways. ... (i)
After filling the unit?s place, any of the four remaining digits can take the ten?s place.
This can be done in 4 ways. ... (ii)
After filling in ten?s place, hundred?s place can be filled from any of the three remaining digits.
This can be done in 3 ways. ... (iii)
So,by counting principle, the number of 3 digit numbers = 5x 4 x 3 = 60
- 1. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options- A. 54
- B. 64
- C. 63
- D. 36 Discuss
- 2. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together
Options- A. 50000
- B. 40500
- C. 5040
- D. 50400 Discuss
- 3. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
Options- A. 1260
- B. 210
- C. 210 x 6!
- D. 1512 Discuss
- 4. In the below word how many words are there in which R and W are at the end positions? RAINBOW
Options- A. 120
- B. 180
- C. 210
- D. 240 Discuss
- 5. If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ?X? as the answer. If no such word can be formed, give ?Z? as the answer.
Options- A. T
- B. X
- C. N
- D. R Discuss
- 6. Find the number of ways to arrange 4 people in groups of 3 at a time where order matters?
Options- A. 20
- B. 16
- C. 24
- D. 36 Discuss
- 7. Find the number of ways to arrange 6 items in groups of 4 at a time where order matters?
Options- A. 720
- B. 640
- C. 740
- D. 360 Discuss
- 8. Find the number of ways to take 20 objects and arrange them in groups of 5 at a time where order does not matter.?
Options- A. 57090
- B. 15540
- C. 15504
- D. 23670 Discuss
- 9. How many ways are there to select a subcommittee of 7 members from among a committee of 17?
Options- A. 19000
- B. 19448
- C. 19821
- D. 19340 Discuss
- 10. Determine the total number of five-card hands that can be drawn from a deck of 52 cards.
Options- A. 2589860
- B. 2598970
- C. 2598960
- D. 2430803 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 63
Explanation:
Required number of ways =
Correct Answer: 50400
Explanation:
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =7!/2!= 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 3!/5!= 20 ways.
Required number of ways = (2520 x 20) = 50400.
Correct Answer: 1260
Explanation:
A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210×6= 1260
Correct Answer: 240
Explanation:
When R and W are the first and last letters of all the words then we can arrange them in 5!ways. Similarly When W and R are the first and last letters of the words then the remaining letters can be arrange in 5! ways.
Thus the total number of permutations = 2 x 5! = 2 x 120 = 240
Correct Answer: R
Explanation:
The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ?R?.
Correct Answer: 24
Explanation:
P(4,3)= = 24
Correct Answer: 360
Explanation:
6P4 = 6! / (6-4)! = 360
Correct Answer: 15504
Explanation:
= 15504
Correct Answer: 19448
Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,7)= 19,448
Correct Answer: 2598960
Explanation:
When a hand of cards is dealt, the order of the cards does not matter. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. Thus cards are combinations. There are 52 cards in a deck and we want to know how many different ways we can put them in groups of five at a time when order does not matter. The combination formula is used.
C(52,5) = 2,598,960
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