EGN 3443 Probability and Statistics for Engineers USF BULL R

EGN 3443 Probability and Statistics for Engineers

USF BULL RUNNER EXERCISE

How many distinct arrangements are there of USF?

How many distinct arrangements are there of BUL₁L₂ and BULL?

How many distinct arrangements are there of R₁UN₁N₂ER₂ and RUNNER?

How many distinct arrangements are there of EXERCISE?

How many distinct 3-letter arrangements are there of ABCDEFGH?

How many distinct 3-letter sets are there of ABCDEFGH? [Note that {a, b, c}, {a, c, b},   {b, a, c}, {b, c, a}, {c, a, b}, and {c, b, a} all represent the same set.]

How many distinct r-object arrangements can be selected from n objects? How many distinct r-object sets can be selected from n objects?

Solution

How many distinct arrangements are there of USF?

= 3!

= 6 arrangements

How many distinct arrangements are there of BUL1L2 and BULL?

=>

For BUL1L2 = 4! = 24 ways

For BULL = 4! / 2! = 24 / 2 = 12 ways

How many distinct arrangements are there of R1UN1N2ER2 and RUNNER?

=> R1UN1N2ER2 = 6! = 720 ways

RUNNER => 6! / (2! * 2!)

= 720 / 2 * 2

= 180 ways

How many distinct arrangements are there of EXERCISE?

=> Since E is repeated thrice

we have : 8! / 3! ways

= 6720 ways

How many distinct 3-letter arrangements are there of ABCDEFGH?

= Different three letter arrangements = Permutations

= ⁸P₃

= 8! / (8-3)!

= 8! / 5!

= 8 * 7 * 6

= 336 ways

How many distinct 3-letter sets are there of ABCDEFGH? [Note that {a, b, c}, {a, c, b},   {b, a, c}, {b, c, a}, {c, a, b}, and {c, b, a} all represent the same set.]

=>

This is a combination of 3 letters :

⁸C₃ = 8! / ( 3! * 5!)

= 56 ways

How many distinct r-object arrangements can be selected from n objects? How many distinct r-object sets can be selected from n objects?

+> r-object arrangements = ⁿP_r = n! / (n-r)!

r - objec sets = ⁿC_r = n! / (r! * (n-r)! )

Hope this helps.