Final answer:
To find the number of distinct ways to distribute 7 gifts among 10 children, without any child receiving more than one gift, we use the combinations formula C(10, 7), yielding 120 distinct results.
Step-by-step explanation:
The question is asking how many distinct ways 7 gifts can be distributed among 10 children with the condition that no child receives more than one gift. This is a problem of calculating combinations without repetition, which is a part of combinatorial mathematics.
To solve this, we use the formula for combinations which is C(n, k) = n! / (k!(n - k)!). In this case, n is the total number of children (10) and k is the number of gifts (7). So the number of distinct results is C(10, 7).
Calculating this gives us:
10! / (7!(10 - 7)!) = 10! / (7!3!) = (10×9×8) / (3×2×1) = 120 distinct results.