In how many sequences can 7 players throw a ball such that the youngest player does not go last-.
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Answer: C. 4320
Explanation
Total unconstrained arrangements of seven players throwing a ball equal seven factorial or fifty zero forty. Arrangements where the youngest player is restricted to the final position equal six factorial or seven twenty. Subtracting seven twenty from fifty zero forty produces the correct valid sequence count of forty three twenty. Permutations count the number of ways to arrange a set of distinct objects in order. The factorial of a positive integer represents the product of all integers up to that number. The principle of complementary counting simplifies problems with negative conditional constraints.
Sports tournament schedulers use permutation mathematics to determine valid team batting or playing orders. Computer algorithms generate permutations while ensuring certain protocol endpoints remain fixed. Event planners organize participant sequences while respecting specific seniority or age restrictions. Option a represents a rounded estimation rather than the exact combinatorial calculation. Option b counts only the restricted arrangements instead of subtracting them from the total. Option d results from minor arithmetic subtraction errors in the final step.
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- Mathematics
- Category
- Mathematics
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- Difficulty
- medium
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