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Question
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
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Solution
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is 35.
Explanation:
The following may be the arrangement of (–) and (+)
(–) (+) (–) (+) (–) (+) (–) (+) (–) (+) (–) (+) (–)
Therefore, ‘+’ sign can be arranged only is 1 way because all are identical.
And 4(–) signs can be arranged at 7 places in 7C4 ways
∴ Total number of ways = 7C4 × 1
= `(7 xx 6 xx 5 xx 4)/(4 xx 3 xx 2 xx 1) xx 1`
= 35 ways
Hence, the value of the filler is 35.
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