How many eight-letter sequences are possible that use the letters f, i, t, t, i, n, g, s
A)720
B) 4
C) 20,160
D) 16
E) 10,080

Question

How many eight-letter sequences are possible that use the letters f, i, t, t, i, n, g, s   
A)720
B) 4
C) 20,160
D) 16
E) 10,080

Quizplus · Accepted Answer

The sequence has 8 letters with "t" and "i" each appearing twice. The formula for permutations of a multiset is $n! / (n_1! \cdot n_2! \cdot ... \cdot n_k!)$, where $n$ is the total number of items, and $n_1, n_2, ..., n_k$ are the counts of each unique item. Here, $n = 8$, $n_1 = n_2 = 2$ (for "t" and "i"), so the number of sequences is $8! / (2! \cdot 2!) = 40,320 / 4 = 10,080$.

How Many Eight-Letter Sequences Are Possible That Use the Letters