separately and then add the respective numbers. There will be as many flag signals as there are ways of filling in vacant places in succession by the flags available. By Multiplication rule, the number of ways is × = . Similarly, there will be as many flag signals as there are ways of filling in vacant places in succession by the flags.
MATHEMATICS The number of ways is × × = . Continuing the same way, we find that The number of flag signals = × × × = and the number of flag signals = × × × × = Therefore, the required no of signals = + + + = . EXERCISE . .
How many -digit numbers can be formed from the digits , , , and assuming that repetition of the digits is allowed? repetition of the digits is not allowed? . How many -digit even numbers can be formed from the digits , , , , , if the digits can be repeated?
. How many -letter code can be formed using the first letters of the English alphabet, if no letter can be repeated? . How many -digit telephone numbers can be constructed using the digits to if each number starts with and no digit appears more than once?
. A coin is tossed times and the outcomes are recorded. How many possible outcomes are there? .
Given flags of different colours, how many different signals can be generated if each signal requires the use of flags, one below the other? . Permutations In Example of the previous Section, we are actually counting the different possible arrangements of the letters such as ROSE, REOS, ..., etc. Here, in this list, each arrangement is different from other.
In other words, the order of writing the letters is important. Each arrangement is called a permutation of