How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
There are many ways to form 4-letter codeusing the first 10 letters of the English alphabet. The first place can be occupied by any of the 10 alphabets, thus, there are 10 ways to fill the first place in the 4-letter code.
Since the repetition of letters is not allowed, thus there are only 9 letters left after the filling of first place. So, the second place can be occupied by any of the remaining 9 letters. Thus, there are 9 possible ways to fill the second place in the 4-letter code.
In the same way, the alphabets left after filling two places are 8. This means that there are 8 possible ways to fill the third place in the 4-letter code. Similarly, from the remaining 7 alphabets, the number of ways tooccupy the fourth place is 7.
The multiplication principle states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the given order is m × n .
Hence, by the multiplication principle the total number of ways to form 4-letter code using the first 10 letters of the English alphabet is,
10 × 9 × 8 × 7 = 5040
Thus, 4-letter code with 10 letters of English alphabet can be formed in 5040 ways with no repetition.
There are many ways to form 4-letter codeusing the first 10 letters of the English alphabet. The first place can be occupied by any of the 10 alphabets, thus, there are 10 ways to fill the first place in the 4-letter code.
Since the repetition of letters is not allowed, thus there are only 9 letters left after the filling of first place. So, the second place can be occupied by any of the remaining 9 letters. Thus, there are 9 possible ways to fill the second place in the 4-letter code.
In the same way, the alphabets left after filling two places are 8. This means that there are 8 possible ways to fill the third place in the 4-letter code. Similarly, from the remaining 7 alphabets, the number of ways tooccupy the fourth place is 7.
The multiplication principle states that if an event can occur in m different ways and follows another event that can occur in n different ways, then the total number of occurrence of the events in the given order is
Hence, by the multiplication principle the total number of ways to form 4-letter code using the first 10 letters of the English alphabet is,
Thus, 4-letter code with 10 letters of English alphabet can be formed in 5040 ways with no repetition.
