Question 6 of 42beginner🔧 ApplyNumerical2 marks

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Correct Answer

20

Exercise: EXERCISE 6.1 | Q: 6 | (Page 5)
For More Understanding

Explanation

This question is directly solved in Example 4 of the textbook context. The question asks for signals using exactly 2 flags from 5 different flags. This is a permutation problem where order matters (the flag on top is different from the flag below). The solution uses the multiplication principle: for the first position (top flag), there are 5 choices, and for the second position (bottom flag), there are 4 remaining choices. Therefore, the total number of signals = 5×45 \times 4 = 20.

Solution Steps

  1. Step 1: Identify that we need to fill 2 vacant places (one below the other) using 5 different flags.

  2. Step 2: The upper vacant place can be filled in 5 different ways by any one of the 5 flags available.

  3. Step 3: After filling the upper place, the lower vacant place can be filled in 4 different ways by any one of the remaining 4 flags.

  4. Step 4: By the multiplication principle, the total number of different signals = 5×45 \times 4 = 20.

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