Answer and Step-by-step explanation:
The number of ways to choose 7 letters without replacement from 12 distinct letters, where the order of the choices is not relevant, is given by the combination formula. The combination formula is:
nCr = n! / (r!(n - r)!)
where n is the total number of elements, r is the number of elements to be chosen, and n! is the factorial symbol, which means the product of all the positive integers from 1 to n.
In this case, n = 12 and r = 7. So, the number of ways to choose 7 letters without replacement from 12 distinct letters, where the order of the choices is not relevant, is:
12C7 = 12! / (7!(12 - 7)!) = 792
Therefore, there are 792 ways to choose 7 letters without replacement from 12 distinct letters, where the order of the choices is not relevant.