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Permutations and Combinations

Short Answer Type

131. In how many of the distinct permutations of the latter in MISSISSIPPI do the four I’s not come together?

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132. In how many ways can the letters of word ‘ASSASSINATION’ be arranged so that all the S’s are together?

164 Views

133. In how many ways can the letters of word ‘ASSASSINATION’ be arranged so that the arrangements be such that they start with O and end with T and the S’s are all together ?

107 Views

Long Answer Type

134.

How many different words, with or without meaning can be formed, by using the letters of the word ‘HARYANA’? Also, find as to:

(a) how many of these begin with H and end with N?

(b) in how many of these H and N are together?

591 Views

Short Answer Type

135. Find the number of words with or without which can be made using all the letters of the word ‘AGAIN’. If these words are written as in a dictionary, what will be the 50th word?

107 Views

136. The letters of the word ‘RANDOM’ are arranged as in a dictionary. What is the rank of word ‘RANDOM’?

469 Views

Long Answer Type

137.

How many different words can be formed by using the letters of the word ‘ALLAHABAD?

(a) In how many of these do the vowels occupy even positions.

(b) In how many of these, the two L’s do not come together?

526 Views

Short Answer Type

138.

In how many ways can 8 students be seated

(a) in a straight line (b) in a circle?

181 Views

139. In how many ways can 5 persons be seated around a round table so that two of them must always be together?

Tie the two
Number of arrangements = $space straight P presuperscript 2 subscript 2 space equals space 2 factorial space equals space 2$
Mix with remaining
Now, we have 3 + 1 = 4 persons to sit around a round table.
The number of permutations = (4 - 1)! = 3! = 6
Hence, the total number of arrangments when the two persons sit together
= 2 x 6 = 12

105 Views

140.

Find the number of permutations of 6 students sitting around a round table.

(a) In how many of these arrangements are three of the students sit together ?

(b) In how many of the arrangements, three of the students do not sit all together ?

91 Views