Respuesta :
Answer:
84 words.
Step-by-step explanation:
We are asked to find the number of permutations that can be formed using 3 letters at a time, using the letters in the word ADDITION.
Since order matters in permutations, so the repetition of same words is not allowed.
The number of permutations of n objects taken r at a time is determined by the following formula:
[tex]\text{Number of permutations}=P(n,r)=\frac{n!}{(n-r)!}[/tex]
Since 2 letters are repeated so we can choose 3 letters from 8 letters as:
[tex]\text{Number of permutations that can be formed using 3 letters at a time}=\frac{8!}{(8-3)!*2!*2!}[/tex]
[tex]\text{Number of permutations that can be formed using 3 letters at a time}=\frac{8!}{5!*2!*2!}[/tex]
[tex]\text{Number of permutations that can be formed using 3 letters at a time}=\frac{8*7*6*5!}{5!*2*1*2*1}[/tex]
[tex]\text{Number of permutations that can be formed using 3 letters at a time}=4*7*3[/tex]
[tex]\text{Number of permutations that can be formed using 3 letters at a time}=84[/tex]
Therefore, there are 84 words that can be formed using 3 letters at a time.
Answer:
336
Step-by-step explanation:
8P3 = 8! / (8-3)!
8P3 = 8! / 5!
8P3 = 8x7x6x5x4x3x2x1 / 5x4x3x2x1
5x4x3x2x1 cancels itself out so you're left with
8P3 = 8x7x6 = 336
