Difference between revisions of "Combination Activity 1"
(Created page with "=== Objectives === Students will be able to calculate a combination using a formula. Students will have an understanding of what a combination is. Students understand the di...") |
m (added Category:Permutations and Combinations using HotCat) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 16: | Line 16: | ||
'''Problem''' | '''Problem''' | ||
| − | |||
Say, three people are | Say, three people are | ||
eligible to win two similar prizes. | eligible to win two similar prizes. | ||
| − | |||
'''Method''' | '''Method''' | ||
| − | |||
Now the students can | Now the students can | ||
reason this out. Three people are eligible to win two prizes. Both | reason this out. Three people are eligible to win two prizes. Both | ||
| Line 29: | Line 26: | ||
what the students come up with for this combination. | what the students come up with for this combination. | ||
| − | + | '''Win''' | |
| − | '''Win | ||
Prize 1 (W) Win Prize 2 (W) Loss | Prize 1 (W) Win Prize 2 (W) Loss | ||
| − | (LS) | + | (LS) |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
{| border="1" | {| border="1" | ||
| Line 43: | Line 34: | ||
| | | | ||
Shariff | Shariff | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
|- | |- | ||
| | | | ||
Ashwini | Ashwini | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
|- | |- | ||
| | | | ||
Rakesh | Rakesh | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''LS''' | '''LS''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
| | | | ||
'''W''' | '''W''' | ||
| − | |||
|} | |} | ||
| Line 142: | Line 112: | ||
Answer : '''190''' | Answer : '''190''' | ||
| + | |||
| + | [[Category:Permutations and Combinations]] | ||
Latest revision as of 11:02, 30 January 2020
Objectives
Students will be able to calculate a combination using a formula.
Students will have an understanding of what a combination is.
Students understand the difference between permutations and combinations
Estimated Time
Prerequisites/Instructions, prior preparations, if any
Materials/ Resources needed
Counting Sticks (Match sticks), Paper, Pencil
Process (How to do the activity)
Problem
Say, three people are eligible to win two similar prizes.
Method
Now the students can reason this out. Three people are eligible to win two prizes. Both prizes are exactly the same. Break out the counting sticks and see what the students come up with for this combination.
Win Prize 1 (W) Win Prize 2 (W) Loss (LS)
|
Shariff |
W |
W |
W |
LS |
W |
LS |
|
Ashwini |
W |
LS |
W |
W |
LS |
W |
|
Rakesh |
LS |
W |
LS |
W |
W |
W |
Students should notice that columns are repeating when the prize is similar and hence there are only 3 outcomes. Students will be told this is the way “choose” as it is sometimes called, to pick or unordered outcomes from n possibilities. Stress the unordered part.
Extend this problem by asking the students how 20 people can win 5 prizes. This will be difficult to do manually and hence the formula will need to be used.
Evaluation at the end of the activity
Student tries to solve the following problem.
First tries it in a table with classroom of 3 students and 2 students needing to stay back after school and then uses the formula.
In a classroom filled with 20 students, 2 will be selected to stay after school and help their teacher for a programme.How many combinations are possible?
Answer : 190