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How many different words can be formed by jumbling the letters in the word  MISSISSIPPI  in which no two S are adjacent?

  • Option 1)

    7\cdot \, ^{6}C_{4}\cdot \; ^{8}C_{4}

  • Option 2)

    8\cdot \, ^{6}C_{4}\cdot \; ^{7}C_{4}

  • Option 3)

    6\cdot \, 7\cdot \; ^{8}C_{4}

  • Option 4)

    6\cdot \, 8\cdot \; ^{7}C_{4}

 

Answers (1)

best_answer

As we have learned

Number of arrangement of like and alike objects -

The number of arrangements that can be formed using n objects out of which r, q and p are identical objects then total number of arrangements=\frac{n!}{p!\ q!\ r!}

Ex. ALLAHABAD

A\rightarrow4

L\rightarrow2

\therefore\ \; \frac{9!}{4!\ 2!}

-

 

 Arrange M,I,I,I,P,P,I

No. of ways = \frac{7!}{2141}= 7 \cdot \frac{6 !}{2141}= 7 \cdot _{4}^{6}\textrm{C}

 Now arrange 4 'S' in the gaps = _{4}^{8}\textrm{C}

\therefore

= 7 \cdot _{4}^{6}\textrm{C}  _{4}^{8}\textrm{C}


Option 1)

7\cdot \, ^{6}C_{4}\cdot \; ^{8}C_{4}

Option 2)

8\cdot \, ^{6}C_{4}\cdot \; ^{7}C_{4}

Option 3)

6\cdot \, 7\cdot \; ^{8}C_{4}

Option 4)

6\cdot \, 8\cdot \; ^{7}C_{4}

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gaurav

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