How many 4-letter codes can be formed using t | vedclass

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(A) The number of ways to form a $4$-letter code is equivalent to the number of ways to fill $4$ vacant places in succession using the first $10$ lett

Vedclass · Accepted Answer

$5040$

Vedclass · Answer

(A) The number of ways to form a $4$-letter code is equivalent to the number of ways to fill $4$ vacant places in succession using the first $10$ letters of the English alphabet,where repetition is not allowed.The first place can be filled in $10$ ways.The second place can be filled in $9$ ways.The third place can be filled in $8$ ways.The fourth place can be filled in $7$ ways.By the multiplication principle,the total number of ways is $10 	imes 9 	imes 8 	imes 7 = 5040$.Thus,$5040$ four-letter codes can be formed.

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

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