Answer :
In 840 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 4 at a time.
Given that,
The letter word; "PAYMENT"
We have to determine,
In how many ways the letter word "PAYMENT" be arranged if the letters are taken 4 at a time.
According to the question,
A permutation is a mathematical calculation of the number of ways a particular set can be arranged, where the order of the arrangement matters.
Here, The letter word; ''PAYMENT''
The number of words in the letter word "PAYMENT" is 7.
The number of arranged the letter word "PAYMENT" are taken 4 at a time. by using formula;
[tex]^nP_r = \dfrac{n!}{(n-r)! \ r!}[/tex]
Where, Set of letter word = n = 7, and arrangement of 'r' objects r = 4.
Substitute the values in the formula;
[tex]^nP_r = \dfrac{n!}{(n-r)!}\\\\^7P_4 = \dfrac{7!}{(7-4)! \ }\\\\^7P_4= \dfrac{7!}{3! \ }\\\\^7P_4 = \dfrac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times1}{ 3 \times2 \times1 }\\\\^7P_4 = 840 \ ways[/tex]
Hence, In 840ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 4 at a time.
To know more about Permutation click the link given below.
https://brainly.com/question/15811099