Question

║⊕QUESTION⊕║
Pure mathematics is the poetry of logical ideas
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CLASS 11
PERMUTATIONS AND COMBINATIONS
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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?

Answer 1

Step-by-step explanation:

8C4*7!/ 4!2!

=8C4*7*6!/4!2!

=7*8C4*6C4

=7350 ways

Answer 2

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}\mid}}}}$

There are restriction of no two 'S' to be together

So leaving space for 'S' let's arrange remaining words.

$\underline{ \: \: \: \: \: } \: \underline{ M } \: \underline{ \: \: \: \: \: } \: \underline{ I } \: \underline{ \: \: \: \: \: } \: \underline{ I } \: \underline{ \: \: \: \: \: } \: \underline{I } \: \underline{ \: \: \: \: \: } \: \underline{ P } \: \\ \underline{ \: \: \: \: \: } \: \underline{ P } \: \underline{ \: \: \: \: \: } \: \underline{ I } \: \underline{ \: \: \: \: \: } \:$

We can arrange the seven letters in,

$\frac{7 ! }{4 ! \times 2! }$

We can place 'S' in vacant boxes

There are four 'S' in word MISSISSIPPI

So we have option of selecting any four places

$^{n} C_r = ^{8}C_4 = \frac{8 !}{4!(8 - 4)!}$

So your answer is,

$\frac{7!}{4! \times 2!} \times ^{8} C_4 \\ \\ \frac{7 \times \cancel6 \times 5 \times \cancel4! }{ \cancel4! \times \cancel2 \times 1} \times \frac{ \cancel8 \times 7 \times \cancel6 \times 5}{ \cancel4 \times \cancel3 \times \cancel2} \\ \\ 105 \times 70 \\ \\ \huge\boxed{ 7350 \: \: ways}$

$\boxed{ \begin {minipage} {7 cm} Formula \: for \: ^{n}P_r \: and \: ^{n}C_r \\ \\ ^{n}P_r = \frac{ n !}{(n-r) !} \\ \\ ^{n}C_r = \frac{n !}{ r ! (n-r) ! } \end {minipage}}$