Permutation: n Different Things Taken r at a Time

Q.

The number of all possible matrices of order $3\times 3$ with each entry 0 to 1 is
(a)27
(b)18
(c)81
(d)512

Q. Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

1. 69760
2. None of these
3. 99748
4. 30240

Q.

In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets. more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes ?

Q.

If P(9, r)= 3024, find r.

Q.

Find the total number of ways in which six '+' and four '–' signs can be arranged in a line such that no two '–' signs occur together.

Q.

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?

Q.

The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is

1. 1958

2. 1956

3. 16

4. 64

Q.

A, P, R, X, S, and Z are sitting in a row. S and Z are in the center. A and P are at the ends. R is sitting to the left of A. Who is to the right of P?

1. A

2. X

3. S

4. Z

Q.

The number of ways in which ten candidates A1, A2........A10 can be arranged in vertical row(column) when

1)if A1, A2 are next to each other. [9!.2!]

2)if A1 is just above A2. [9!]

3)if A1 is always above A2. [10!/2!]

4)if A1 is always above A2 and A2 is above A3 is.[10!/3!]

5)if A1, A2, A3 sit together in a specified order is. [8!]

Please explain solution in detail for the 3, 4, 5 specially. And kindly don't close the question for whatsoever reason as i typed it with a lot of hard work.[ Answers in bracket.]

Q.

If all permutations of the letters of the word AGAIN are arranged as in dictionary, then fiftieth word is equal to:

1. NAAGI

2. NAGAI

3. NAAIG

4. NAIAG

Q.

Make the greatest and the smallest $4-\mathrm{digit}$ number using any four different digits with the given condition. $4$ is always in the thousands place.

Q.

The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is

1. 1200

2. 2400

3. 14400

4. 1440

Q. In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes

1. 1024
2. 625
3. 120
4. 600

Q.

If P(n, 5)=20.P(n, 3), find n.

Q.

Prove that:
(i) $\frac{n!}{(n-r)!}$
= n(n-1)(n-2)...(n-(r-1))
(ii) $\frac{n!}{(n-r)!r!}+\frac{n!}{(n-r+1)!(r-1)!}$
= $\frac{(n+1)!}{r!(n-r+1)!}$

Q.

The number of permutations of $4$ letters that can be made out of the letters of the word EXAMINATION is

1. $2454$

2. $2452$

3. $2450$

4. $1806$

Q.

Ajay writes five letters to his five friends and addresses the corresponding .The number of ways can the letters be placed in the envelopes so that at least 2 of them are in the wrong envelopes

Q.

In a class there are 27 boys and 14 girls. The teacher want to select 1 boy and 1 girl to represent the class in a function. In how many ways teacher can make this selection ?

Q. How many four letter words can be formed from the letters of the word "LOGARITHMS", if repetation is not allowed ?

Q.

If $n_{P-4}=360$, find the value of n.

Q.

How many numbers greater than $40000$ can be formed from the digits $2,4,5,5,7?$

1. $12$

2. $24$

3. $36$

4. $48$

Q.

The number of $4$ digit odd numbers, that can be formed by using the digits $0,1,2,3,4,5,6$ when the repetition is allowed, is

1. $120$

2. $300$

3. $420$

4. $20$

Q.

If P (15, r-1): P(16, r-2)=3:4, find r.

Q.

In how many ways can six persons be seated in a row ?

Q.

If P(n, 5) : P(n, 3) = 2:1, find n.

Q.

How many three letter words can be made using the letters of the word 'ORIENTAL' ?

Q.

In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?

Q.

The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included?

1. $3700$

2. $3720$

3. $4340$

4. None of these

Q.

If A and B are two matrices of the order 3 $\times m$ and 3 $\times$n respectively and m = n, then order of matrix (5A - 2B) is
(a) $m\times 3$ (b) $3\times 3$ (c) $m\times n$
(d) $3\times n$

Q.

In how many ways can five children stand in a queue ?