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Quantity A: k is an integer between 1 and 100, inclusive what is probability tha
Quantity A: k is an integer between 1 and 100, inclusive what is probability tha
游客
2024-01-12
62
管理
问题
Quantity A: k is an integer between 1 and 100, inclusive what is probability that k×(k+1)×(k+2)×(k+3)×(k+4) is divisible by 20
Quantity B: 1
选项
A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.
答案
C
解析
k是从1到100的整数,包含1,100,对于表达式k×(k+1)×(k+2)×(k+3)×(k+4)来说,是5个连续的正整数相乘,5个连续的正整数中至少有两个连续的偶数,必然是4的倍数;5个连续的正整数中至少有一个是5的倍数。因此这个乘积必然能够被20整除,所以概率为1。选择C。
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