A Math teacher requires each student to solve 5 out of 15 problems. Of the 15 problems, 3 are Statistics, 7 are in Algebra, and 5 are in Geometry. In how many ways can a student select each of the following for the 5 problems: 5 Algebra problems? 5 Statistics or Geometry problems? 3 Statistics and 2 Geometry problems? 5 Geometry problems?
Answers
Answer:
Use this method
Step-by-step explanation:
A Tea Party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. 4 Persons wish to sit on one particular and 2 on the other side. How many arrangements are possible?
Let the Sides be A and B
Let 4 persons wish to sit at side A. They can sit in 8P4 ways.
Similarly 2 Persons can sit on other side in 8P2
Now we are left with 10 places and 10 persons. So they can be arranged in 10! Ways.
Total Number of Arrangements = 8P4 X 8P2 X 10!
Given : A Math teacher requires each student to solve 5 out of 15 problems.
3 are Statistics, 7 are in Algebra, and 5 are in Geometry
To Find : In how many ways can a student select each of the following for the 5 problems:
5 Algebra problems
5 Statistics or Geometry problems
3 Statistics and 2 Geometry problems
5 Geometry problems
Solution:
3 are Statistics, 7 are in Algebra, and 5 are in Geometry
5 Algebra problems out of 7 Algebra can be selected in
⁷C₅ = 21 ways
5 Statistics or Geometry problems
Total 3 are Statistics 5 are in Geometry Hence
=> 0 S + 5G ³C₀* ⁵C₅ = 1
1 S + 4G ³C₁* ⁵C₄ = 15
2S + 3G ³C₂* ⁵C₃ = 30
3S + 2G ³C₃* ⁵C₂ = 10
1 + 15 + 30 + 10 = 56 ways
3 Statistics and 2 Geometry problems
3S + 2G ³C₃* ⁵C₂ = 10 Ways
5 Geometry problems
⁵C₅ = 1 ways
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