Difference between revisions of "2021 AMC 12A Problems/Problem 15"
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==Problem== | ==Problem== | ||
| − | + | A choir direction must select a group of singers from among his <math>6</math> tenors and <math>8</math> basses. The only requirements are that the difference between the number of tenors and basses must be a multiple of <math>4</math>, and the group must have at least one singer. Let <math>N</math> be the number of different groups that could be selected. What is the remainder when <math>N</math> is divided by <math>100</math>? | |
| − | + | ||
| − | + | <math>\textbf{(A) } 47\qquad\textbf{(B) } 48\qquad\textbf{(C) } 83\qquad\textbf{(D) } 95\qquad\textbf{(E) } 96\qquad</math> | |
| − | == | + | |
| − | + | ==Video Solution by Punxsutawney Phil== | |
| + | https://youtube.com/watch?v=FD9BE7hpRvg | ||
| + | |||
==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=14|num-a=16}} | {{AMC12 box|year=2021|ab=A|num-b=14|num-a=16}} | ||
| + | |||
| + | [[Category:Intermediate Combinatorics Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 14:25, 11 February 2021
Problem
A choir direction must select a group of singers from among his 
tenors and 
basses. The only requirements are that the difference between the number of tenors and basses must be a multiple of 
, and the group must have at least one singer. Let 
be the number of different groups that could be selected. What is the remainder when is divided by 
?
Video Solution by Punxsutawney Phil
https://youtube.com/watch?v=FD9BE7hpRvg
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 14 |
Followed by Problem 16 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
