Math Problem Statement
Solution
This problem is asking for the number of ways to arrange all 8 members of a club for a photograph. The members are:
Since all 8 members are to be lined up, we are asked to find the number of possible permutations of these 8 people.
The number of permutations of distinct objects is given by (n factorial). In this case, .
Let me calculate .The number of ways to arrange the 8 members of the club for the photograph is ways.
Would you like further explanation or have any questions about this?
Here are some related questions for practice:
- How many ways can 6 out of the 8 members be selected and then arranged for a photograph?
- If two members must always stand next to each other, how many ways can the group be arranged?
- If the arrangement is circular (for a round photograph), how many distinct ways can they be arranged?
- If Jim and Ashley must not stand next to each other, how many arrangements are possible?
- How many ways can 3 members be chosen from the 8 members for a smaller photograph?
Tip: Remember that factorials grow very quickly, and even small numbers like result in large values like 40,320!
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Math Problem Analysis
Mathematical Concepts
Permutations
Factorial
Formulas
P(n) = n!
Theorems
Permutation Theorem
Suitable Grade Level
Grade 9-12