Permutations And Combinations

In how many ways can 4 letters be posted in 5 letter boxes?
1. $5^{4}$
2. $4^{5}$
3. $4 \times 5$
4. None of these
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2.
1. $3 \times 2 \times 1$
2. $3^{5}$
3. $2 \times 3^{4}$
4. None of these
The number of permutations of n different things taking r at a time when 3 particular things are to be included is:
1. ${}^{n - 3}P_{r - 3}$
2. ${}^{n - 3}P_{r}$
3. ${}^{n}P_{r - 3}$
4. $r! {}^{n - 3}C_{r - 3}$
The number of words that can be formed out of the letters of the word 'COMMITTEE' is:
1. $\frac{9!}{{(2!)}^{3}}$
2. $\frac{9!}{{(2!)}^{2}}$
3. $\frac{9!}{(2!)}$
4. $9!$
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
1. $4^{4}$
2. $4 \times 4$
3. $4!$
4. All of these
Write $\sum_{r = 0}^{m} {}^{n + r}C_{r}$ in the simplified fowm.
1. ${}^{n + m}C_{n + 1}$
2. ${}^{n + m + 1}C_{n + 1}$
3. ${}^{n + 1}C_{n + 1}$
4. None of these
Write the value of $\sum_{r = 1}^{6} {}^{56 - r}C_{3} + {}^{50}C_{4}$ :
1. ${}^{56}C_{4}$
2. ${}^{56}C_{3}$
3. ${}^{50}C_{3}$
4. ${}^{50}C_{4}$
If ${}^{m}C_{1} = {}^{n}C_{2}$ , then:
1. 2m = n
2. 2m = n(n + 1)
3. 2m = n(n - 1)
4. 2n = m(m - 1)
If ${}^{n}C_{r} + {}^{n}C_{r + 1} = {}^{n + 1}C_{x}$ , then x = ?
1. r
2. r - 1
3. n
4. r + 1
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to:
1. 60
2. 120
3. 7200
4. None of these
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISHNA is:
1. 324
2. 341
3. 359
4. 360
The number of arrangements of the word "DELHI" in which E precedes I is:
1. 30
2. 60
3. 120
4. 59
The number of five-digit telephone numbers having at least one of their digits repeated is:
1. 90000
2. 100000
3. 30240
4. 69760
If $C_{0} + C_{1} + C_{2} + . . . . . . + C_{n} = 256$ , then ${}^{2 n}C_{2}$ is equal to:
1. 56
2. 120
3. 28
4. 91
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:
1. 6
2. 9
3. 12
4. 18
The number of different ways in which a man can invite one or more of his 6 friends to dinner is:
1. 30
2. 63
3. 120
4. 15
A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together is:
1. 164
2. 112
3. 140
4. None of these
In how many ways can a mixed doubles tennis game be arranged from a group of 10 players consisting of 6 men and 4 women?
1. 90
2. 120
3. 48
4. 180
The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is:
1. 410
2. 356
3. 260
4. 95
Numbers greater than 1000 but not greater than 5000 are to be formed with the digits 0, 1, 2, 3, 5, allowing repetitions, the number of possible numbers is:
1. 365
2. 356
3. 260
4. 95
The number of all three digit even numbers such that if 5 is one of the digits then next digit is 7 is:
1. 370
2. 365
3. 360
4. None of these
A coin is tossed n times, the number of all the possible outcomes is:
1. P (n, 2)
2. 2n
3. C (n, 2)
4. $2^{n}$
The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is:
1. 90
2. 72
3. 98
4. None of these
If ${}^{n}P_{5} = 60 {}^{n - 1}P_{3}$ , then n is:
1. 12
2. 10
3. None of these
4. 6
The number of ways in which the 6 faces of a cube can be painted with 6 different colours is:
1. 30
2. 6 !
3. 12
4. 6
The number of distinguishable ways in which the 4 faces of a regular tetrahedron can be painted with 4 different colours is:
1. 4
2. None of these
3. 24
4. 2
The number of ways in which n ties can be selected from a rack displaying 3n different ties is:
1. None of these
2. $\frac{(3 n)!}{n! (2 n)!}$
3. (3n) !
4. $3 \times n!$
Find Rank of word ‘wife ‘among the words that can be formed with its letters and arranged as in dictionary is:
1. 24
2. 8
3. 18
4. 4
The number of even numbers that can be formed by using all the digits 1, 2, 3, 4, and 5 (without repetitions) is:
1. None of these
2. 1250
3. 48
4. 162
The number of all numbers that can be formed by using some or all of the digits 1, 3, 5, 7, 9 (without repetitions) is:
1. 325
2. 32
3. None of these
4. 120
If $P (n - 1, 3) : P (n, 4) = 1 : 9$ , then n is:
1. 6
2. 7
3. 8
4. 9
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is:
1. 24
2. 30
3. 125
4. 100
The total number of arrangements of the letters of the word BANANA in which two N's come together:
1. 10
2. 20
3. 30
4. 40
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together.
1. None of these
2. $7! \times 7$
3. $7! \times 7!$
4. $7! \times 6!$
If ${}^{20}C_{r} = {}^{20}C_{r - 10}$ , then ${}^{18}C_{r}$ is equal to:
1. 4896
2. 816
3. 1632
4. 1800
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is:
1. 45
2. 40
3. 39
4. 38
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
1. 60
2. 20
3. 15
4. 125
If ${}^{n + 1}C_{3} = 2 . {}^{n}C_{2}$ , then n is equal to:
1. 3
2. 4
3. 5
4. 6
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is:
1. $4! \times 3!$
2. $4!$
3. $3! \times 3!$
4. None of these
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
1. 6
2. 20
3. 60
4. 120

Permutations And Combinations

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