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How many 4-letter code words are possible using the first 10 letters of the english alphabet,if no letter can be repeated?

$\begin{array}{1 1}(A)\;\text{5000 ways}\\(B)\;\text{5040 ways}\\(C)\;\text{5060 ways}\\(D)\;\text{5080 ways}\end{array}$

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First letter of the code word can be selected in 10 ways.After the selection of first letter,we have 9 letters.Hence the second letter can be selected in 9 ways.According to FPC,first two letters can be selected in $10\times 9$ ways
Similarly third letter can be selected in 8 ways,under the fourth letter can be selected in 7 ways.According FPC,number of ways of selecting four letters out of 10 letters of english alphabet.
$\Rightarrow 10\times 9\times 8\times 7$ways
$\Rightarrow 5040$ways
Hence (B) is the correct answer.
answered May 13, 2014

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