stats 4-6

Question 1

STATS 4-6

Fundamental counting rule

Answer 1

given the first event can occur m ways and the second event can occur n ways, the number of ways that two events can occur is given by this formula:
m*n, 5 digit pincode on a 10 key keypad:

10 5

Question 2

STATS 4-6

Factorial rule

Answer 2

n! is the number of different permutations (order counts) of n different items when all n of them are selected. ex: number of ways letters A,B,C,D,E can be arranged.

5! = 54321 =120

Question 3

STATS 4-6

0!

Answer 3

= 1

Question 4

STATS 4-6

permutations (when all items are different)

Answer 4

arrangements in which different sequences of the same items are counted separately. only r of them are selected without replacement

• order does matter
• n P r
• n = total numbers
• r = number being chosen

Question 5

STATS 4-6

Permutations rule (when some items are identical to others)

Answer 5

number of different permutations when n items are available and all n are selected without replacement, but some of the items are identical to others. ex: if 10 letters (a,a,a,a,b,b,c,c,d,e,) are available and all 10 of them are to be selected without replacement, the number of different permutations 10!/4!2!2! = 37,800

Question 6

STATS 4-6

combinations

Answer 6

number of different combinations (order doesn’t matter) when n different items are available, but only r of them are selected without replacement. ex: if the 5 letters (A,B,C,D,E) are available, and 3 of them are to be selected without replacement the number of combinations are as follows:

nCr = 5C3 = 10