wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is


Open in App
Solution

Find the number of words that satisfy the given arrangement conditions

The word SYLLABUS has the following letters,

SS,Y,LL,A,B,U. (Five different letters, two repeated twice)

We need 4 letter words with 2 similar and 2 dissimilar letters.

The two similar letters can be chosen in C12 ways.

The two dissimilar letters can be chosen in C25 ways.

Now the four letters can be arranged in 4!2! ways.

Hence, the total number of words satisfying the given arrangement =C12×C25×4!2!

=21×5×4×3×22×3×2×4×3×22

=240

Hence, 240 four letter words are formed such that two of the letters are alike and two are different.


flag
Suggest Corrections
thumbs-up
36
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving an Equation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon