Eight digit number can be formed using all the digits 1,1,2,2,3,3,4,5.
(i) A number is selected at random then the probability such that no two identical digits appear together
Text Solution
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(i) Identical letters are 1,1,2,2,3,3. Total words = 
= 5040
Number of words in which all identical letters are together = 5!
Number of words in which only exactly two pair of identical digits appear together = 
× 3 = 720
Number of words in which only one pair of identical digits appear together (1, 1) together
= 
× 3= 1980
Now number of words in which no two identical digits appear together = 5040 – (1980 + 720 + 120) = 2220
Probability = 
= 
(ii) Number of words in which only exactly two pair of identical digits appear together = 
× 3 = 720
Total words = 
= 5040 ; Probability = 
= 
.
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