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oee [108]
3 years ago
5

3 of the digits 0-9 are chosen randomly by a computer what is the probability that it will choose 3 sequential digits?

Mathematics
1 answer:
Sindrei [870]3 years ago
7 0

Answer:

B. 1/15

Step-by-step explanation:

The number of ways in which we can select x elements from a group of n elements is calculated as:

nCx=\frac{n!}{x!(n-x)!}

So, the number of ways in which a computer can select 3 digits is calculated as:

10C3=\frac{10!}{3!(10-3)!}=120

Because there are 10 digits from 0 to 9.

Then, from that 120 options there are 8 that have 3 sequential digits. These options are:

{0,1,2} {1,2,3} {2,3,4} {3,4,5} {4,5,6} {5,6,7} {6,7,8} {7,8,9}

So, the probability that it will choose 3 sequential digits is equal to:

P=\frac{8}{120}=\frac{1}{15}

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