[1956] How many signals can be made using 6 different coloured flags when any number of them can be hoisted

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How many signals can be made using 6 different coloured flags when any number of them can be hoisted at a time?

1956

1720

2020

1822

Explanation:

Given that any number of flags can be hoisted at a time. Hence we need to find out number of signals that can be made using 1 flag, 2 flags, 3 flags, 4 flags, 5 flags and 6 flags and then add all these.

Number of signals that can be made using 1 flag

= $^6P_{1}$ =6

Number of signals that can be made using 2 flags

=$ ^6P_{2} $

=6×5=30

Number of signals that can be made using 3 flags

=$ ^6P_{3}$

=6×5×4=120

Number of signals that can be made using 4 flags

=$ ^6P_{4} $

=6×5×4×3=360

Number of signals that can be made using 5 flags

= $^6P_{5}$

=6×5×4×3×2=720

Number of signals that can be made using 6 flags

= $^6P_{6 }$

=6×5×4×3×2×1=720

Therefore, required number of signals

=6+30+120+360+720+720=1956

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