SOLUTION: Dear math teacher,
I have solved the following problem in two ways. Please let me know, whether each way is correct. Thank you for your time and effort.
1.)
nC15 = nC11
n
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Permutations
-> SOLUTION: Dear math teacher,
I have solved the following problem in two ways. Please let me know, whether each way is correct. Thank you for your time and effort.
1.)
nC15 = nC11
n
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Question 475561: Dear math teacher,
I have solved the following problem in two ways. Please let me know, whether each way is correct. Thank you for your time and effort.
1.)
nC15 = nC11
nCr = nCn-r
nC15 = nC(n-15) = nC11
Here is where I need help. Why do we simply "drop" n and C from nC(n-15) = nC11
and say:
n-15 = 11
n=26
2.)
nC15 = nC11
nC15 = nC11 = nC(n-11)
Here again, why do we simply "disregard" n and C in nC15 = nC11 = nC(n-11)
to get
15 = n-11
n=26
Thank you again for your time. Have a wonderful evening.
Yours respectfully,
I. Answer by scott8148(6628) (Show Source):
the solution technique here is somewhat analogous to solving simultaneous equations using substitution
you can use x in terms of y or y in terms of x
when you talk about "dropping" or "disregarding"; we are not losing operations here
we are extracting equalities from a notational format so that we can solve them
if I told you that ___ sin(28º) = sin(x - 13º) ___ how would you find x?
the sin format is "dropped" to leave a solvable equality
