Math

Question 1

what is the sum of all consecutive numbers from 1 to n?

Answer 1

n(n+1)/2

Question 2

what is the sum of all consecutive numbers from 0 to n-1?

Answer 2

n(n-1)/2

Question 3

define combination

Answer 3

a counting technique for number of ways to pick certain items from a set to expand into a larger set where ordering of the items per item in the larger set matters.

Question 4

define permutation

Answer 4

a counting technique for number of ways to pick certain items from a set to expand into a larger set where ordering of the items per item in the larger set matters.

a good way to remember is that a “combination lock” is a MISNOMER. it should be a permutation lock because order matters!

Question 5

combination formula without repetition

Answer 5

nCr = n!/(r!(n-r)!)

e.g. a lottery ticket!

Question 6

permutation formula without repetitions

Answer 6

n! / (n-k)!

just multiply the number of choices at each instance

Question 7

permutation formula with repetitions

Answer 7

n^k

just the number of spaces available is k

Question 8

combination formula WITH repetition

Answer 8

i don’t think there’s a general formula

see here: https://www.mathsisfun.com/combinatorics/combinations-permutations.html

e.g. coins in your pocket (5,5,5,10,10,10)