Applied Test Series

Question

A Professor tells 3 Jokes in his maths class each year. How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?_________    

 

 

Answer 1

$\binom{n}{3}\geq 12$

$\frac{n!}{(n-3)!*3!}\geq 12$

$\frac{n*(n-1)*(n-2)}{6}\geq 12$

$n*(n-1)*(n-2)\geq 72$

Considering $n$$=5$ we get $5*4*3=60$$\ngeqslant 72$

Now considering $n=6$ we get $6*5*4= 120$$> 72$.

$\therefore$ Minimum number of jokes needed $=$ $6$.