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Expert: Scott A Wilson
Subject: Maths Application Example ?
Question: QUESTION: Dear Prof Scott

The Above Attached Example of Children becomes which Maths application ?

Multiplication
Probability
Permutation
Combination
Ratio and Proportion
etc

Thanks & Regards,
Prashant S Akerkar
Image: children

ANSWER: I have attached a file with the total number of ways of getting each case.
The 1st column is the number of children, the 2nd column in the number of males,
the 3rd column is the number of females, the 4th column is the number of combinations, and
the last column is the combinations listed out.

Image: kids

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Scott

Thank you. Unable to view the file attached.

Can you send me the file at my email address :



Thanks & Regards,
Prashant S Akerkar
Answer: There is no e-mail address in this message, so I will type it out in the message
for 3, 4, and 5 chilren.  For one and two, the totals are correct.

For three, we should have
M M M
M M F
M F M
M F F
F M M
F M F
F F M
F F F
so that we have 1 with 3 males, 3 with 2 males, 3 with 1 male, and 1 with no males.
That is, 1 3 3 1 for the totals, and the sum is 1+3+3+1 = 8 = 2^3.

For four, we should have
M M M M
M M M F
M M F M
M M F F
M F M M
M F M F
M F F M
M F F F
F M M M
F M M F
F M F M
F M F F
F F M M
F F M F
F F F M
F F F F
so there total for 4 males is 1, 3 males is 4, 2 males is 6, 1 male is 4, and 0 males is 1.
That is 1 4 6 4 1 for the totals, and the sum is 1+4+6+4+1 = 16 = 2^4.

For five it would be
M M M M M
M M M M F
M M M F M
M M M F F
M M F M M
M M F M F
M M F F M
M M F F F
M F M M M
M F M M F
M F M F M
M F M F F
M F F M M
M F F M F
M F F F M
M F F F F
F M M M M
F M M M F
F M M F M
F M M F F
F M F M M
F M F M F
F M F F M
F M F F F
F F M M M
F F M M F
F F M F M
F F M F F
F F F M M
F F F M F
F F F F M
F F F F F
so there is 1 with 5 males, 5 with 4 males, 10 with 3 males,
10 with 2 males, 5 with 1 male, and 0 with no males.
That is 1 5 10 10 5 1 for the totals, and the sum is 1+5+10+10+5+1 = 32 = 2^5.

For 6 the totals would be 1 6 15 20 15 6 1, sum = 64 = 2^6.
For 7 the totals would be 1 7 21 35 35 21 7 1, sum = 128 = 2^7.
For 8 the totals would be 1 8 28 56 70 56 28 8 1, sum = 256 = 2^8.
For 9 the totals would be 1 9 36 84 126 126 84 36 9 1, sum = 512 = 2^9.

Getting these is similar to counting in base 2 with leading 0's.
For five kids, it would be
00001
00010
00011
00100
00101
00110
00111
01000
01001
01010
01011
01100
01101
01110
01111
10000
10001
10010
10011
10100
10101
10110
10111
11000
11001
11010
11011
11100
11101
11110
11111
with 0=males and 1=female.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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