|Expert:||Scott A Wilson|
|Subject:||Maths Application Example ?|
The Above Attached Example of Children becomes which Maths application ?
Ratio and Proportion
Thanks & Regards,
Prashant S Akerkar
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.
---------- 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
with 0=males and 1=female.
This is Scotto, signing out now.
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