IN how many ways can the letters in MISSISSIPPI be arranged so that no two Is are adjacent?

The solution is allegedly

But I don't see the logic to this solution. Any insights would be greatly appreciated.

Thanks, MD

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- November 28th 2011, 11:34 PMMathsdogCombinatorics question
IN how many ways can the letters in MISSISSIPPI be arranged so that no two Is are adjacent?

The solution is allegedly

But I don't see the logic to this solution. Any insights would be greatly appreciated.

Thanks, MD - November 29th 2011, 12:19 AMFernandoRevillaRe: Combinatorics question
: Consider the four I's as a block, then we have seven elements:*Hint*

We have arrangements of those seven elements. Now, move conveniently the four I's. - November 29th 2011, 02:37 AMMathsdogRe: Combinatorics question
Hey, thanks for your reply FernanoRevilla. That makes sense. (n.b. I left an extra P out of MISSISSIPPI, but have now edited it in). But I still dont see where the comes from. If the four had to remain in a block then the solution would be but if any of the positions can be chosen for any of the Is then some of these will contain adjacent Is and others will not eg. MISISISISPP It seems to me this will be included in the factor. No?

Thanks again, MD - November 29th 2011, 04:10 AMPlatoRe: Combinatorics question
- November 29th 2011, 05:31 AMFernandoRevillaRe: Combinatorics question
- November 29th 2011, 06:35 AMSorobanRe: Combinatorics question
Hello, Mathsdog!

Quote:

In how many ways can the letters in MISSISSIPPI be arranged

so that no two I's are adjacent?

The solution is allegedly:

Arrange the letters in a row.

. . There are: arrangements.

Insert a space before, after and between the seven letters:

. .

Choose 4 of the 8 spaces and insert the I's.

. . There are:. choices.

Therefore, there are:. ways.