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Determine the number of paths from the o...

Determine the number of paths from the origin to the point (9, 9) in the cartesian plane which never pass through (5,5) in paths consisting only of steps going 1 unit North and 1 unit East.
Comprehension
A committee of 12 is to be formed from 9 women and 8 men such that atleast 5 women have to be included in the committee.

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MOTION-THEORY AND EXERCISE BOOK-EXERCISE -3
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  16. In how many ways 8 persons can be seated on a round table (a) If two...

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  17. Determine the number of paths from the origin to the point (9, 9) in t...

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  18. The number of ways of forming the committee, is

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  19. The number of committees in which women are in majority, is

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  20. There are nine different books on a shelf, four red and five are green...

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