Combinatorics

9000148907

Level: 
A
A bowl contains \(12\) different gummy-bears and \(20\) different sweet-drops. Anne can choose either one sweet-drop or one gummy-bear. From the rest, Jane can choose one sweet-drop and two gummy-bears. Anne wants to provide a maximum of the possibilities for Jane's choice. What should Anne choose?
sweet-drop
gummy-bear
Both possibilities give the same result.

9000148908

Level: 
A
There are seven different yellow apples, eight different green apples and ten different red apples. How many ways are there to choose three apples, if we wish to have three apples of different colors?
\(10\cdot 8\cdot 7=560\)
\(\frac{10\cdot 8\cdot 7} {2}=280 \)
\((10 + 8 + 7)\cdot 2=50\)
\(10 + 8 + 7=25\)

9000148909

Level: 
A
There are \(24\) girls and \(8\) boys in the class. How many ways are there to designate a president and vice-president of the class if it is required that one of the position will be held by a boy and the other one by a girl?
\(24\cdot 8\cdot 2=384\)
\(24\cdot 8=192\)
\(\frac{32!} {2!\; 30!}=496\)
\(\frac{32!} {24!\; 8!}=10\:518\:300\)

9000141502

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. The number of \(5\)-permutations with repetition is \(1024\). Find \(n\). (The term „\(k\)-permutation with repetition” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects, when each object can be chosen more than once.)
\(4\)
\(5\)
\(2\)

9000141501

Level: 
B
Let \(A\) be set with \(n\) mutually different elements. If \(n\) is increased by \(2\), then number of \(3\)-permutations is increased by \(384\). Find \(n\). (The term „\(k\)-permutation” stands for an ordered arrangement of \(k\) objects from a set of \(n\) objects.)
\(8\)
\(64\)
\(32\)