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141. 4 boys and 3 girls are to sit around a round table. In how many ways can this be done so that no two girls sit together.

Let the boys sit around the round table.

Number of arrangements = (4 - 1)! =3! = 6 ...(i)
There are 4 seats for the girls and there are 3 girls.

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∴ Total number of permutations when no two girls are together = 6 x 24 = 144

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142.

(a) In how many ways can a girl make a garland with 8 flowers?

(b) In how many ways can a girl make a necklace with 4 red, 3 green and 2 blue beads?

116 Views

143. Find the number of words formed by arranging the letters of the word:

(a) INDIA (b) ARRANGE (c) EXERCISES

(d) SERIES (e) INTERMEDIATE

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Long Answer Type

144.

Find the number of arrangements of the letters of word ‘INDEPENDENCE’. How many of these words:

(a) start with P? (b) the vowels always occur together?

(d) begin with I and end with P?

228 Views

Short Answer Type

145.

How many words can be formed using the letters of word ‘PARALLEL’ so that the L’s

(a) come together (b) do not come together ?

145 Views

146. How many words can be formed out of the letters of the word ‘UNIVERSITY’, in which all the vowels remain together?

92 Views

147. The letters of the word LATE are arranged as per the dictionary pattern. Find the rank of the word LATE.

140 Views

148. In how many ways can the letters of the word ‘ARRANGE’ be arranged so that the two R’s are never together?

94 Views

149. How many words can be formed from the letters of the word ‘SERIES’ which:

(a) start with R and end with I (b) start with S and end with S?

91 Views

Long Answer Type

150. How many different words can be formed using letters of the word ‘MATHEMATICS’.

(a) How many of them begin with C?

(b) How many begin with T?

133 Views