Q. 11

# Given 7 flags of different colors, how many different signals can be generated if a signal requires the use of two flags, one below the other?

Answer :

Given: seven flags are available and out of which two are needed to make a signal.

From this, we can say, that we have to select two flags out of seven and arrange these two flags to get one signal.

So, number of ways to select two flags out of seven is ^{7}C_{2}. These flags can be arranged in 2! ways one below the other

Hence total number of signals possible are ^{7}C_{2} × 2! = 42

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Which of the following are true :

(2 + 3)! = 2! + 3!

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