(a) Show that the number of arrangements of 25 distinct objects is an integer multiple of \(5 ^ { 6 }\).
(b) Explain how this shows that the number of arrangements of 25 distinct objects is a whole number of millions.
(a) Calculate the values of
INT(720 \(\div 25\) )
INT(720 \(\div 125\) ).
(b) Deduce the largest power of 10 that is a factor of 720!
Use the inclusion-exclusion principle to find the number of integers from 1 to 720 that are not divisible by either 2 or 5 .