Quandaries
and Queries
Who is asking: Other
Level: Secondary
Question:
Show that
10C0 + 10C1 + 10C2 + 10C3+.....10C10 =1024
Hint:
Combination formula is
nCr = Fatorial(n)/Factorial(r)*factorial of(n-r)
Hi,
That's a terrible hint! What you are counting is the number of ways to choose 0 or 1 or 2 or ... or 10 things from 10 things, all the possibilities. This is the same as counting the total number of subsets of a set of size 10. How do we count that? Well, we have 2 choices whether or not to include the first element, we have 2 choices whether or not to include the 2nd element, we have 2 choices whether or not to include the 3rd element, ..., we have 2 choices whether or not to include the 10th element; in total 2x2x2x...x2 = 210 =1024 ways.
Penny