Answer to Question #117089 in Combinatorics | Number Theory for Priya

Question

How many words of length 10 can you form where no letter is repeated?

Answer 1

Solution.

Since the Italian alphabet contains 21 letters, the number of words of 10 letters can be found:

$A_n^k=\dfrac{n!}{(n-m)!} -$ Placement from n to k ;

$A_{21}^{10}=\dfrac{21!}{(21-10)!}=\dfrac{21!}{11!}=12\sdot13\sdot14\sdot15\sdot16\sdot17\sdot18\sdot19\sdot\ 20 \sdot21= ‬$

$=1 279 935 820 800‬;$

Answer: $A_{21}^{10}=1 279 935 820 800‬.$