Permutations MATHS - Permutations

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is.

The number of five-digit telephone numbers having at least one of their digits repeated is:

The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is:

A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is:

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

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.

If P(5, r) = P(6, r - 1), find r

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?

If the letters of the word 'MOTHER' are written in all possible orders and these words are written out as in a dictionary, find the rank of the word 'MOTHER'.

The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?

In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

1. The vowels always occupy even places?
2. The relative order of vowels and consonants do not alter?

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac.

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