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geniusboy [140]
4 years ago
5

How many three digit numbers are there that have the property that one digit is the sum of the other two digits?

Mathematics
1 answer:
mash [69]4 years ago
4 0
Ways to get an even sum:
22 odd 11 even.
33 even.
First case:
First see that there are three posiblities for the place the even number takes: (the first number cant be 0 because then it would not be a 3 digit number. Therefore there are (4∗5∗5)+2(5∗5∗5)(4∗5∗5)+2(5∗5∗5) ways
second case: all even. there are 4∗5∗54∗5∗5 ways to do it therefore the total is 100+250+100=450100+250+100=450 numbers
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Probability extension: Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised t
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Answer:

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Step-by-step explanation:

The complete question is;

<em>Counting: Grading One professor grades homework by randomly choosing 5 out of 12 homework problems to grade.</em>

<em>(a) How many different groups of 5 problems can be chosen from the 12</em>

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<em>(b)Probability extension: Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded?</em>

<u>In (a)</u>

<u></u>

Apply the formula

\frac{n!}{(n-r)!(r!)}

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substitute values

=\frac{12!}{(12-5)!(5!)} \\\\\\=\frac{12!}{(7!)(5!)} \\\\\\=\frac{12*11*10*9*8}{5*4*3*2*1} \\\\\\=\frac{95040}{120} \\\\\\=792

In (b)

If Jerry did only 5 problems of one assignment then the probability  will be

\frac{5}{12} *\frac{4}{11} *\frac{3}{10} *\frac{2}{9} *\frac{1}{8} =\frac{1}{792}

<em />

<em />

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