Advertisements
Advertisements
Question
In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?
Advertisements
Solution
5 boys can be seated among themselves in 5P5 = 5! Ways. After this arrangement, we have to arrange the three girls in such a way that in between two girls there atleast one boy.
So the possible places girls can be placed with the × symbol given below.
× B × B × B × B × B ×
∴ There are 6 places to seated by 3 girls which can be done 6P3 ways.
∴ Total number of ways = 5! × 6P3
= 120 × (6 × 5 × 4)
= 120 × 120
= 14400
APPEARS IN
RELATED QUESTIONS
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
The number of permutations of n different things taking r at a time when 3 particular things are to be included is
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.
