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Question
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
Options
1958
1956
16
64
Solution
1956
Number of permutations of six signals taking 1 at a time = 6P1
Number of permutations of six signals taking 2 at a time = 6P2
Number of permutations of six signals taking 3 at a time = 6P3
Number of permutations of six signals taking 4 at a time = 6P4
Number of permutations of six signals taking 5 at a time = 6P5
Number of permutations of six signals taking all at a time = 6P6
∴ Total number of signals
\[= \frac{6!}{5!} + \frac{6!}{4!} + \frac{6!}{3!} + \frac{6!}{2!} + \frac{6!}{1!} + 6! \]
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