The number of ways in which an arrangement of 
letters of the word 
can be made is
Text Solution
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We have got 
i.e. 
types of letters. We have to form words of 
letters.
We consider four cases
All 
different: Selection 
Arrangement 
Two different and two alike:
and 
in 
ways. Having chosen one pair we have to choose 
different lettersout of the remaining 
different letters in 
ways. Hence the number of selections is
. Each of the above 
selections has 
letters out of which 
are alike and they canbe arranged in 
ways.
Hence number of arrangements is 
.
(iii) 
like of one kind and 
of other:
Out of these sets of three like letters we can choose 
sets in 
ways. Each such
selection will consist of 
letters out of which 
are alike of one kind, 
of the other. They can bearranged in 
ways.
Hence the number of arrangements is 
(iv) 
alike and 
different:
There is only one set consisting of 
like letters and it can be chosen in 
way. The remainingone letter can be chosen out of the remaining 
types of letters in 
ways.
Hence the number of selection 
. Each consists of 
letters out of which 
are alike andeach of them can be arranged in 
ways.
Hence the number of arrangements is 
.
From 
, 
, 
and 
, we get
Number of selections 
Number of arrangements 
.
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