Question Detail
Question
What is the number of signals that can be sent by 6 flags of different colours, taking one or more at a time?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Since the flags are of different colours and the order matters (a signal 'red-blue' is different from 'blue-red'), this is a permutation problem. We need to find the sum of permutations of choosing 1 flag, 2 flags, ..., up to 6 flags.Number of signals = 6P1 + 6P2 + 6P3 + 6P4 + 6P5 + 6P66P1 = 66P2 = 6 × 5 = 306P3 = 6 × 5 × 4 = 1206P4 = 6 × 5 × 4 × 3 = 3606P5 = 6 × 5 × 4 × 3 × 2 = 7206P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720Total signals = 6 + 30 + 120 + 360 + 720 + 720 = 1956.
Hint
The problem asks for 'one or more' flags, and the order of flags matters for a signal. Calculate P(n,r) for each r from 1 to n and sum them up.