Home
Class 12
MATHS
Find the number of permutations of lette...

Find the number of permutations of letters `a ,b ,c ,d ,e ,f,g` taken all together if neither beg nor cad pattern appear.

Text Solution

Verified by Experts

The total number of permutations without any restriction is 7!
`n(U)=7!=5040`
Let n(A) be the number of permutations in which 'beg' pattern always appears
`"b e g a c d f"`
i.e., `n(A)=5!=120`
and let `n(B)` be the number of permutations in which 'cad'
c a d b e f g
i.e., `n(B)=5!=120`
Now, `n(A capB)=` number of permutations inwhich 'beg' and 'cad' pattern appear
b e g c a d f
i.e., `n(A capB)=3!=6`
Hence, the number of permutations in which 'beg' annd 'cad' patterns do not appears is `n(A'capB')`
or `n(A'capB')=n(U)-n(AcupB)`
`=n(U)-[n(A)+n(B)-n(A capB)]`
`=5040-120-120+6=4806`
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of permutations of the letters of the word SIMPLETON taken all at a time is :

Find the number of combinations and permutations of four letters taken from the word EXAMINATION.

Find the number of permutations that can be had from the letters of the word 'OMEGA' (i) O and A occuping end places. (ii) E being always in the middle.

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

If a denotes the number of permutations of (x+2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things taken all at a time such that a=182b c , find the value of xdot

Find the number of different selections of 5 letters, which can be made from 5A's,4B's,3C's,2D's and 1E

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels occur together .

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels do not occur together.

The total number of words that can be formed using all letters of the word 'RITESH' that neither begins with I nor ends with R, is

Total number of words that can be formed using all letters of the word "DIPESH" that neither beginns with 'I' nor ends with 'D' is equal to