1.3 Pascal's Triangle

Question 1

n>C>0

Answer 1

1

there is only one way to choose nothing from n!

Question 2

n>C>1

Answer 2

n

when choosing 1 object from n objects, there are n possibilities to choose from

Question 3

n>C>n-1

Answer 3

n

when choosing 1 less than n from n objects, there are n possible objects to leave out

Question 4

n>C>n

Answer 4

1

to select n objects from n objects, you must select everything, hence 1!

Question 5

Properties of

Pascal’s Triangle

3 answers

Briefly outline each

Answer 5

Symmetry of Combinations:
From the Triangle, n>C>r = n>C>n-r

Additive Property of Combinations:
In any subsequent row, an entry is the sum of the two entries on either side of it in the previous row.
n>C>r = n-1>C>r-1 + n-1>C>r

Total # of Subsets from n Objects:
(Including empty set and universal set itself): 2^n
(Including empty set but excluding universal set; proper subsets): 2^n-1

Question 6

Binomial Theorem

Answer 6

(x+y)^n = (n>0).x^n.y^0 + (n>1).x^n-1.y^1 + (n>2).x^n-2.y^2 … (n>n).x^0.y^n

combinations are equal to numbers in nth row of pascal’s triangle

x begins power of n and decreases while y starts power of zero and increases

Question 7

Determine all the coefficiens in (binomial expansion)

Chat: finding coefficients of binomial expansion question

Question 8

Find the coefficient of one term in expression

Chat: Finding coefficient of one term in binonial expansion question