Problem Solving

What is the best way to answer this question?

How many different 6-letter sequences are there that consist of 1 A, 2 B's, and 3 C's?

(A) 6
(B) 60
(C) 120
(D)360
(E) 720

Cheers,

Different sequences = nPr / x! * y! where x! and y! are terms that are repeated.

==>6! / (2! * 3!)
==>60, Answer is B

Different sequences = nPr / x! * y! where x! and y! are terms that are repeated.

Correction: Note that the formula for computing the total number of orders when terms are repeated is actually: n!/x!*y! where x and y are the repeated terms. (nPr is for when we are pulling out ordered subgroups of size "r" from a bigger group of size "n").

How many ways of arranging the letters in the word SLOT?

How many letters in total? 4. Any repeated letters? No. So, this is simply 4!

What about the word SLOTS?

How many letters in total? 5. But "S" shows up twice. So, this will be 5!/2!