Five integers are picked from 0 to 20, with possible repetitions, such that…
2026
Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20. Ignoring permutations, the number of ways to pick these five integers is _____
Answer: B. 1 — Let the sorted integers be a≤ b≤ c≤ d≤ e. The median gives c=18, and the mean gives a+b+c+d+e=60. Since 20 is the unique mode, it must occur more often than…
- A.
0
- B.
1
- C.
2
- D.
3
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Correct answer: B
Let the sorted integers be a≤ b≤ c≤ d≤ e. The median gives c=18, and the mean gives a+b+c+d+e=60. Since 20 is the unique mode, it must occur more often than any other value. Because the median is 18, at most two entries can exceed 18, so 20 can occur at most twice. To be a mode, 20 must occur at least twice, hence exactly twice: d=e=20. Then a+b+18+20+20=60, so a+b=2. The other values must each occur at most once, so a<b<18. The only nonnegative integer solution is a=0 and b=2. Thus the only unordered selection is {0,2,18,20,20}, giving 1 way.