Discussion
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- Question
- In how many ways, a committee of 3 men and 2 women can be formed out of a total of 4 men and 4 women?
Options- A. 15
- B. 16
- C. 20
- D. 24
- Correct Answer
- 24
ExplanationTotal number of ways = 4C3 x 4C2 = [4! / {3! x 1!}] x [4! /{2! x 2!}]
= (4 x 4 x 3 x 2 x 1) / (2 x 2)
= 4 x 6
= 24 - 1. How many necklaces of 12 beads can be made from 18 beads of various colours?
Options- A. [118 x 13!] / 2
- B. [110 x 14! ] / 2
- C. [119 x 13!] / 2
- D. [110 x 12!] / 2 Discuss
- 2. In how many different ways, 5 boys and 5 girls can sit on a circular table, so that the boys and girls are alternate?
Options- A. 2880
- B. 2800
- C. 2680
- D. 2280 Discuss
- 3. 20 persons were invited to a party. In how many ways, they and the host can be seated at a circular table?
Options- A. 18 !
- B. 19 !
- C. 20 !
- D. Couldn't be determined Discuss
- 4. Find the number of ways, in which 12 different beads can be arranged to form a necklace .
Options- A. 11 !/2
- B. 10 !/2
- C. 12 !/2
- D. Couldn't be determined Discuss
- 5. In how many ways, can the letters of the word 'ASSASSINATION' be arranged, so that all the S are together?
Options- A. 10!
- B. 14! (4!)
- C. 151200
- D. 3628800 Discuss
- 6. In how many ways, a cricket team of 11 players can be made from 15 players, if a particulars player is always chosen?
Options- A. 1835
- B. 1001
- C. 1635
- D. 1365 Discuss
- 7. There is a polygon of 12 sides . How many triangles can be drawn using the vertices of polygon?
Options- A. 200
- B. 220
- C. 240
- D. 260 Discuss
- 8. Find the number of diagonals formed in hexagon .
Options- A. 12
- B. 10
- C. 6
- D. 9 Discuss
- 9. There are 10 points in a plan, out of which 5 are collinear. Find the number of straight lines formed by joining them.
Options- A. 36
- B. 45
- C. 30
- D. 35 Discuss
- 10. In how many ways, 12 balls can be divided between 2 boys, one receiving 5 and the other 7 balls?
Options- A. 1784
- B. 1584
- C. 1854
- D. 1560 Discuss
Permutation and Combination problems
Search Results
Correct Answer: [119 x 13!] / 2
Explanation:
First, we can select 12 beads out of 18 beads in 18C12 ways.
Now, these 12 beads can make a necklace in 11! / 2 ways as clockwise and anti-clockwise arrangements are same.
So, required number of ways = [ 18C12 .11! ] / 2!
= [18C6.11! ] / 2!
= [18 x 17 x 16 x 15 x 14 x 13 x 11! ] / [6 x 5 x 4 x 3 x 2 x 1 x 2!]
= [17 x 7 x 13! ] / 2!
= 119 x 13 !/ 2
Correct Answer: 2880
Explanation:
After fixing up one boy on the table, the remaining can be arranged in 4 ! ways, but boys and girls have to be alternate. There will be 5 places, one place each between two boys. These 5 place can be filled by 5 girls in 5 ! ways .
Hence, by the principle of multiplication, the required number of ways = 4 ! x 5 ! = 2880
Correct Answer: 20 !
Explanation:
Total persons on the circular table
= 20 guests + 1 host = 21
They can be seated in (21 - 1) ! = 20 ! ways .
Correct Answer: 11 !/2
Explanation:
Number of arrangements of beads = (12 - 1) !, but it is not mentioned that either it is clockwise or anti - clockwise .
So, required number of arrangements = [(12 - 1)! ] / 2 = 11 !/2
Correct Answer: 151200
Explanation:
When All S are taken together, then ASSASSINATION has 10 letters .
\
So, 10 letters in total can be arranged in 10 ! ways .
[? All 'S' are considered as 1]
But, here are 3 'A' and 2'I' and 2 'N' .
? Required number of ways = 10 ! / (3 ! x 2 ! x 2 !) = 151200
Correct Answer: 1001
Explanation:
Since, particular player is always chosen. It means that 11 - 1 = 10 players are selected out of the remaining 15 - 1 = 14 players.
? Required number of ways = 14C10
= 14 ! / (10! x 4!)
= (14 x 13 x 12 x 11) / (4 x 3 x 2 x 1)
= 7 x 13 x 11
= 91 x 11
= 1001
Correct Answer: 220
Explanation:
Required number of triangles = 12C3 = (12 x 11 x 10) / 6 = 220
Correct Answer: 9
Explanation:
Hexagon has 6 sides .
? n = 6
? Required number of diagonals = 10C2 - n
= 6C2 - 6
= 6! / [2!(6 - 2)!] - 6 = 6! / (2!4!) - 6
= (6 x 5 x 4!) / (2 x 4!) - 6
= 15 - 6
= 9
Correct Answer: 36
Explanation:
Required number of straight lines
=nC2 - mC2 + 1
Here, n = 10, m = 5
= 10C2 - 5C2 + 1
= 45 - 10 + 1 = 36
Correct Answer: 1584
Explanation:
Here, order is important, then the number of ways in which 12 different balls can be divided between two boys who receives 5 and 7 balls respectively, is = [12! / 5! 7! ] x 2! = 1584
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