Change: **this can be done with a 5 card hand. Just use the 3 card hand as a simpler model.** Example 2. Using exactly ‘r’ objects, with no identical objects. Problem - In how many ways can a 4 colors be drawn from a pack of 24 pencil crayons? Solution   View changes from previous version. (Word count: 819)

Change: r=8r=4 Way1-performed using a calculator Way 2-calculated by hand nCr = n! (n-r)!r! = 24C4 = 24!(24-4)! 4! = 10 626 ways = 24!20!4! = 10 626 waysEither way there are 10 626 ways of drawing   View changes from previous version. (Word count: 843)

Change: a king or queen cards from a deck of 52 cards. Example 3. Not using exactly ‘r’ objects, but with some identical objects. Problem - How many different sums of money can be made using onei $5make bill,with two1 $10penny, 2 billsnickles and one   View changes from previous version. (Word count: 848)

Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 836)

Change: FormulaeFormula Combination notation nCr--> = n! (see example 2 and flowchart) (n-r)!r! Combinations in which some items are identical § (p+1) (q+1) (s+1) …-1 [to remove the null set] (see example 3) § (p+1) (q+1) (s+1) … [to include the null set] (see example 3) Not   View changes from previous version. (Word count: 817)

Change: NCONicoNCCOCoNoIgnore--> or 1. -Retain the null set when the question implies that no object at all can also be selected or states: up to, maximum of… - Remove the null set when the question   View changes from previous version. (Word count: 817)

Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 817)

Change: at least 1 spade. Example 2. Using exactly ‘r’ objects, with no identical objects. Problem - In how many ways can 4 cards be drawn from a deck of 52 cards? Solution - Recall from the flow chart, we use the formula nCr = n! (n-r)!r! n=52; r=4 Way1-performed   View changes from previous version. (Word count: 817)

Change: Way 1 - preformed on a calculator.Way 2 - calculated by hand. Either way there are 270 725 ways of drawing 4 cards from a deck of 52 cards. Example 3. Not using exactly ‘r’ objects, but with some identical objects. Problem - How many   View changes from previous version. (Word count: 814)

Change: There were only format changes (bold, italics, etc.) in this version. See this version for details. (Word count: 816)