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Find the number of ways six '+' and four '-' signs be arranged

Question

Find the number of ways six '+' and four '-' signs be arranged in a line so that no two '-' signs occur together.

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Text solutionVerified

Six

^{'} +^{'}

and four

^{'} -^{'}

are to be arranged. So we will arrange

^{'} -^{'}

in the alternate spaces between

^{'} +^{'}

So we have,

(Refer image)

We have

7

empty spaces where we have to arrange

4

^{'} -^{'}

and so we get,

^{7} P_{4} = 7 \times 6 \times 5 \times 4

But all

^{'} -^{'}

are same so we divide the result by

4!

and So, we get

\frac{^{7} P _{4}}{4 !}

possible ways

= \frac{7 \times 6 \times 5 \times 4}{4 \times 3 \times 2 \times 1} = 7 \times 5 = 35

ways

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Question Text	Find the number of ways six '+' and four '-' signs be arranged in a line so that no two '-' signs occur together.
Answer Type	Text solution:1
Upvotes	150