Permutation under Restriction

Q. The number of ways in which six + signs and four – signs can be arranged in a row so that no two – sings occur together is

1. 
2. 
3. 
4. 6!7!

Q.

The number of four digit numbers that can be formed with the digits $1,2,3,4$ and $5$ in which atleast two digits are identical is

1. $4^5-5!$
2. $5^4-4!$
3. $4^5-5$
4. $5^4-5!$

Q. The number of ways in which five students of different heights can sit in a row so that the tallest and the shortest may not sit together is

1. 24
2. 48
3. 72
4. 14

Q.

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

1. 

2. 

3. 

4. 

Q. There are six period on each working day of a school. The number of ways one can arrange 5 subjects such that each subject is allotted atleast one period.

1. 360
2. 3600
3. 1800
4. 36

Q.

6 women and 5 men are to be seated in a row so that no 2 men can sit together. Number of ways they can be seated is

1. 5! $\times {}^7{P}_5$

2. 5! $\times {}^7{P}_5$

3. 6! $\times {}^7{P}_5$

4. 6! $\times {}^6{P}_5$

Q. How many arrangements of four 3’s two 1’s and two 2’s are there in which 1 occurs before 2?

1. 105
2. 315
3. 420
4. 210

Q. Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with atleast one letter repeated is

1. 
2. 
3. 
4. 

Q. The number of numbers with 9 different non – zero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than the digit in the middle is

1. 48
2. 144
3. 288
4. 576

Q. If a denotes the number of permutations of (x+2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of (x – 11) things taken all at a times and a = 182bc, then x =

1. 15
2. 14
3. 13
   
4. 12