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Find the Total Number of Ways in Which Six '+' and Four '−' Signs Can Be Arranged in a Line Such that No Two '−' Signs Occur Together. - Mathematics

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Question

Find the total number of ways in which six '+' and four '−' signs can be arranged in a line such that no two '−' signs occur together.

Solution

Six '+' signs can be arranged in a row in6!6! = 1 way
Now, we are left with seven places in which four different things can be arranged in 7P4ways.
Since all the four '- ' signs are identical, four '- ' signs can be arranged in7P44!ways, i.e. 35 ways.
Number of ways = 1×35 = 35

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Factorial N (N!) Permutations and Combinations
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Chapter 16: Permutations - Exercise 16.5 [Page 43]

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RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.5 | Q 26 | Page 43

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