Question

The number of three-digit numbers with distinct digits that can be formed using the digits 1, 2, 3, 5, 8, and 9 is ________. (Options are: 24, 60, 120, 210, 336) The probability that both the first digit and the last digit of the three-digit number are even numbers is ________. (Options are: 1/6, 1/15, 2/15, 1/30, 1/42)

Answer 1

There are six digits to choose from, but you're only taking three at a time, so the number of such numbers is

${}_6P_3=\dfrac{6!}{3!}=6\times5\times4=120$

The first and last digits can only be even if the number takes the one of the forms "2 _ 8" or "8 _ 2". The middle number can be any of the remaining four, so there is a total of eight such numbers.

This means the probability of getting a number beginning and ending with an even digits is $\dfrac8{120}=\dfrac1{15}$.

Answer 2

Answer:

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Step-by-step explanation: