Permutations MATHS - Permutations

The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is:

1. 574
2. 36
3. 754
4. 144

The number of ways to arrange the letters of the word CHEESE are:

1. 120
2. 240
3. 720
4. 6

The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is:

1. 60 × 5!
2. 15 × 4! × 5!
3. 4! × 5!
4. None of these.

In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is:

1. 12² − 1
2. 2¹²
3. 2¹² − 1
4. None of these

Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys.

Write the number of words that can be formed out of the letters of the word 'COMMITTEE'.

Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together.

In how many ways 4 women draw water from 4 taps, if no tap remains unused?

Write the number of numbers that can be formed using all for digits 1, 2, 3, 4.

Convert the following products into factorials:
1.3.5.7.9....(2n - 1)

Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?

Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.

How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?

A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, if no digit is repeated? How many of these will be even?

In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?

In how many ways can 7 letters be posted in 4 letter boxes?

A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?

Find the number of words formed by permuting all the letters of the following words:
INDIA.

If P(n, 4) = 12 . P(n, 2), find n.

If P(11, r) = P(12, r − 1) find r.

Find the number of words formed by permuting all the letters of the following words:
 CONSTANTINOPLE.

If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.