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प्रश्न
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.
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उत्तर
We have 6 ‘+’ signs:
This creates 7 gaps (slots) where ‘−’ signs can be placed:
-
One before the first ‘+’
-
Five between each pair of ‘+’
-
One after the last ‘+’
(7 slots in total)
We have 4 ‘−’ signs, and no two can be together.
That means each ‘−’ must go into a different slot.
Choose 4 slots out of 7 to place the ‘−’ signs.
The number of ways = `((7),(4)) = 35`
The total number of ways = 35.
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