Home
Class 11
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

Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time ?

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

The number of permutations of the letters of the word 'CONSEQUENCE' in which all the three Es are together 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 permutation of all the letters of the word MATHEMATICS which starts with consonants only.

Number of permutations of 1, 2, 3, 4, 5, 6, 7, 8, and 9 taken all at a time are such that the digit 1 appearing somewhere to the left of 2 3 appearing to the left of 4 and 5 somewhere to the left of 6, is kxx7! Then the value of k is _________.

The number of permutation of all the letters of the word PERMUTATION such that any two consecutive letters in the arrangement are neither both vowels nor both identical is

Find the number of ways in which the letters of word 'MEDICAL' be arranged if A and E are together but all the vowels never come together.

Find the number of seen letter words that can be formed by using the letters of the word SUCCESS so that the two C are together but no two S are together.