Permutation and Combination
Permutation and Combination - Important Points
| 1. | In how many ways 4 persons can be seated on 4 chairs? |
|---|
A. 20
B. 24
C. 26
D. 120
View Answer Discuss Work SpaceAnswer: option b
Explanation:
The number of arrangements = 4! =4 x 3 x 2 x 1 = 24
| 2. | How many five digits numbers divisible by 5 can be formed from digits 2, 1, 0, 7, 5 if the digits are not to be repeated? |
|---|
A. 36
B. 24
C. 42
D. 120
View Answer Discuss Work SpaceAnswer: option c
Explanation:
For divisibility by 5, the digit at unit place should be 0 or 5
There are two cases-
(a) If unit place is 0, the remaining 4 digits can be arranged in 4! = 24 ways
(b) If unit place is 5, the remaining 4 digits can be arranged in 3 x 3! = 18 ways.
So, Total numbers divisible by 5 = 24 + 18 = 42
| 3. | How many three-digit numbers divisible by 3 can be formed out of the digits 3, 4, 5 and 6 if the digits are not to be repeated? |
|---|
A. 18
B. 12
C. 24
D. 36
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Given digits 3, 4, 5 and 6.
Test of divisibility of 3 is that the sum of the digits should be divisible by 3.
Form the given digits, three digits can be 3, 4, 5 or 4, 5, 6.
For each combination of digits, number of numbers
= 3P3 = 3! = 6 ways.
Total number of numbers = 6 + 6 = 12
| 4. | How many numbers greater than 5000 can be made out of the digits 2, 3, 5 and 6 if the digits are not to be repeated? |
|---|
A. 6
B. 12
C. 24
D. 18
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Given digits = 2, 3, 5 and 6
Thousand’s place Hundred’s place Ten’s place Unit’s place
(5 or 6) 2 ways 3 ways 2 ways 1 way
Total number of numbers which are greater than 5000 are = 2 × 3 × 2 × 1 = 12.
| 5. | How may four-digit numbers can be made out of the digits 1, 2, 3 and 9 which are less than 3000, if repetition of the digits allowed? |
|---|
A. 144
B. 288
C. 128
D. 256
View Answer Discuss Work SpaceAnswer: option c
Explanation:
Given digits = 1, 2, 3 and 9.
The largest 4-digit number permitted is 2999.
Since repetition is allowed.
Thousand’s place Hundred’s place Ten’s place Unit’s place
(1 or 2) Any of four Any of four Any of four
2 ways 4 ways 4 ways 4 ways
Total number of numbers that can be formed
= 2 × 4 × 4 × 4 = 128.
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