How many 4-letter codes can be formed using the first 10 letters of the

Question:

How many 4-letter codes can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

 

Solution:

Given: first 10 letters of the English alphabet.

In 4 letter code for first position there are 10 possibilities for second position there are 9 possibilities, for third position there are 8 possibilities and for fourth position there are 7 possibilities since repetition is not allowed.

So total numbers of combination $=10 \times 9 \times 8 \times 7=5040$

 

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