To find the probability that comic E will perform last in a lineup of six comics (A, B, C, D, E, and F), we can consider the total number of possible arrangements (or permutations) of the six comics and the number of arrangements where comic E is last.
- Total Arrangements: The total number of arrangements of six comics is given by the factorial of the number of comics, which is 6! (6 factorial).
\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \]
- Arrangements with E Last: If we want comic E to be last, we can arrange the other five comics (A, B, C, D, and F) in the first five positions. The number of arrangements of these five comics is given by 5! (5 factorial).
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]
- Probability Calculation: The probability \( P \) that comic E performs last is the number of favorable outcomes (arrangements with E last) divided by the total number of arrangements.
\[ P(E \text{ last}) = \frac{\text{Number of arrangements with E last}}{\text{Total arrangements}} = \frac{5!}{6!} = \frac{120}{720} = \frac{1}{6} \]
Thus, the probability that comic E will perform last is:
\[ \boxed{\frac{1}{6}} \]
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