A

2010007005

Level: 
A
A license plate of a car consists of \(7\) symbols so that letters are on the first three positions and digits on remaining four positions, while any used symbol can be repeated. Letters are chosen from \(26\) symbols of the alphabet and digits are chosen from the set \(\{0; 1;\dots; 9\}\). How many such license plates can be set up?
\( 26^3 \cdot 10^4\)
\( 10^3 \cdot 26^4\)
\(36^7\)
\(26\cdot 25\cdot 24\cdot 10^4\)

2010007004

Level: 
A
From a group of \(6\) boys and \(8\) girls we have to select a small group of \(2\) boys and \(4\) girls. How many possibilities exist for this choice?
\(\frac{6!} {4!\, 2!}\cdot \frac{8!} {4!\, 4!}=1\:050\)
\(\frac{6!} {4!}\cdot \frac{8!} {4!}=50\:400\)
\(2\cdot 4=8\)
\(6\cdot 8=48\)