Combinations

End-in-mind/challenge

Sonic advertises that they have over 168,000 drink combinations. Is this correct? How many do they actually have? Parameters:

12 base drinks 16 Add-ins Max of 1 base drink and 6 add-ins

How many ways can you pick 3 pizza topping from the following 4 topping offered (assuming no repeats):

Pepperoni, sausage, Canadian Bacon, Chicken

Combinations

*Use when order does not matter*

The total number of ways of selecting n objects, taking r at a time (order does not matter)

!

( )! !n

n r r

nnC C

rn r r

How many ways can you pick 3 pizza topping from the following 4 topping offered (assuming no repeats):

Pepperoni, sausage, Canadian Bacon, Chicken

What if we only pick 2 toppings?

The cheer coach has to cut the team down from 16 players to 9, how many ways could this be done?

Examples

I need to choose 5 students from those in here today to come to the board. How many ways could I do this?

Examples

How many ways could you deal a 7-card hand from a normal deck of cards?

Examples

How many ways could you deal a 5 card hand with 3 red cards and 2 black cards?

Examples

How many ways could you deal a 7 card hand with all red cards or all black cards?

Examples

How many ways could you deal a 7 card hand with at most 1 diamond?

Examples

10.2 Assignments

End-in-mind/challenge

Sonic advertises that they have over 168,000 drink combinations. Is this correct? How many do they actually have? Parameters:

12 base drinks 16 Add-ins Max of 1 base drink and 6 add-ins