1003024603
Level:
B
Simplify the following expression without using a calculator:
\( \frac{85!+4\cdot84!-84\cdot83!}{2\cdot84!}\)
\( 44 \)
\( 88 \)
\( 66 \)
\( 22 \)
Combinatorics
1003024604
Level:
B
Without using a calculator, identify which of the following values is the greatest one.
the number of ordered arrangements of \( 5 \) objects taking \( 3 \) at a time
the number of unordered selections of \( 3 \) objects out of \( 5 \) different kinds with repetition allowed
the number of ordered arrangements of \( 5 \) objects in which \( 3 \) are identical
the number of unordered selections of \( 3 \) objects out of \( 5 \) objects
1003024605
Level:
B
Simplify the following expression without using a calculator:
\( \frac{91}{13!}+\frac{6}{12!}-\frac1{11!} \)
\( \frac1{12!} \)
\( \frac{96}{13!} \)
\( \frac{85}{13!} \)
\( \frac1{13!} \)
2000002501
Level:
B
Simplify: \( \frac{8!}{6!} \)
\( 56\)
\( 336 \)
\( 8 \)
\(\frac{4}{3} \)
2000002502
Level:
B
Simplify: \( \frac{18!}{19!} \)
\( \frac{1}{19} \)
\( \frac{18}{19} \)
\( 18\)
\( 1 \)
2000002503
Level:
B
Simplify: \( \frac{32!}{32 \cdot 31} \)
\( 30! \)
\( 31! \)
\( 29! \)
\( \frac{1}{31} \)
2000002504
Level:
B
Simplify: \( \frac{50!}{49!+49!} \)
\( 25 \)
\( 100 \)
\( 49! \)
\( \frac{1}{49} \)
2000002505
Level:
B
Simplify: \( \frac{(50-48)!}{(49-49)!} \)
\( 2 \)
\( 1 \)
\( 50! \)
\( \frac{50}{49} \)
2000002506
Level:
B
Simplify: \( \log_{10}(10!)-\log_{10}(9!) \)
\( 1\)
\( 10 \)
\( \log_{10}(9!) \)
\(0\)
2000002701
Level:
B
Simplify for \(n \in \mathbb{N}\): \(\left({n+5\above 0.0pt
n+4} \right)\)
\( n+5\)
\(n+4\)
\(1\)
\(5\)