Advertisements
Advertisements
Question
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
Advertisements
Solution
Since no two men be together they have to be placed between
8 women and before and after the women.
w | w | w | w | w | w | w | w
There are 9 places so the 6 men can be arranged in the 9 places in 9P6 ways.
After this arrangement, the 8 women can be arranged in 8! ways.
∴ Total number of arrangements = (9P6) × 8!
APPEARS IN
RELATED QUESTIONS
Compute `(8!)/(6! xx 2!)`
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
How many 4-digit numbers are there with no digit repeated?
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
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 ways in which 8 distinct toys can be distributed among 5 childrens.
Evaluate each of the following:
P(6, 4)
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
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
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
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`
