Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 3 flags, one below the other?
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Given : 5 flags of different colours
each signal requires the use of 3 flags,
To Find : number of different signals can be generated
Solution:
Total Flags = 5
3 Flags out of 5 can be selected in ⁵C₃
= 5!/3!.2!
= 5 * 4 * 3!/ 3!*2!
= 20/ 2
= 10
3 flags can be arranges in 3! = 6 ways
Total Signals can be generated = 10 * 6 = 60
Direct ways as order of selection matters here
hence ⁵P₃ = 5!/2! = 5 * 4 * 3 = 60
60 different signals can be generated
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