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

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 Multiple Choice QuestionsShort Answer Type

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.
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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?


(a) Number of flowers = 8
     rightwards double arrow                   n = 8
      Number of ways in which the garland can be made

                    space space equals fraction numerator left parenthesis straight n minus 1 right parenthesis factorial over denominator 2 end fraction space equals space fraction numerator 7 factorial over denominator 2 end fraction space equals space 5040 over 2 equals 2520.

(b) Number of beads = (4 red + 3 green + 2 blue) = 9
     Number of ways in which the necklace can be made
                        = fraction numerator begin display style 1 half end style left parenthesis straight n minus 1 right parenthesis factorial over denominator straight p factorial space straight q factorial space straight r factorial end fraction equals 1 half open square brackets fraction numerator 8 factorial over denominator 4 factorial space 3 factorial space 2 factorial end fraction close square brackets

                        =  1 half cross times fraction numerator 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator left parenthesis 4 cross times 3 cross times 2 cross times 1 right parenthesis space left parenthesis 3 cross times 2 cross times 1 right parenthesis space left parenthesis 2 cross times 1 right parenthesis end fraction
                        = 70.

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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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 Multiple Choice QuestionsLong 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?

(c) the vowels never occur together?

(d) begin with I and end with P?

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 Multiple Choice QuestionsShort 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 ?

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146. How many words can be formed out of the letters of the word ‘UNIVERSITY’, in which all the vowels remain together?
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147. The letters of the word LATE are arranged as per the dictionary pattern. Find the rank of the word LATE.
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148. In how many ways can the letters of the word ‘ARRANGE’ be arranged so that the two R’s are never together?
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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?
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 Multiple Choice QuestionsLong 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?

(c) In how many of these vowels occur together?

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