Permutations Maths - Permutations

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'.

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

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?

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.

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if

1. 4 letters are used at a time?
2. All letters are used at a time.
3. All letters are used but first is vowel.

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 '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.