Combinatorics | Number Theory Answers

Find the value of n given that 3n permutation 4 = (n-1)permutation 5

How many 5 letter code words (not necessarily word with sense) can be formed from the letter A B C D E F G H I and J if ? a. The word has at least one vowel

The six graders at Washington middle school research the history of their city this day still gave a presentation to the other students at the school if they were 64 six skaters list all the ways they could have been divided equally into groups of 10 or fewer students

Does there exist a positive integer n such that n^2 − 71 is evenly divisible by 107? Prove
your assertion.

If f is a multiplicative arithmetic function then prove that
f([m, n])f((m, n)) = f(m)f(n)
for all positive integers m and n.
Here [m, n] is the least common multiple of m and n and (m, n) is the
greatest common divisor of m and n.

In how many ways can ball bearings labeled A, B, C and D be
shared by Jacob and Helen in such a way that
1 Jacob gets one ball bearing and Helen gets three
2 They each get two ball bearings?

(a) In how many different ways can the letters of the word wombat be arranged?
(b) In how many different ways can the letters of the word wombat be arranged if the letters wo
must remain together (in this order)?
(c) How many different 3-letter words can be formed from the letters of the word wombat? And
what if w must be the first letter of any such 3-letter word?

The 10 students who completed a special flying course are waiting to see if they will be awarded the one distinctiin or the one merit award for their offers.
In how many ways can the two awards be given if the same student can recieve both awards?
Show full working and the table for the sample space!

mae has more than 3 bracelets she has an even number of bracelets. Is the nimber of braceletstha mae has a prime number or compsite number ?

1.If m={prime number from 5—30}. Write out all the subjects of m

2. Given that k={even number from 1–10}. Find n(k)