How many distinguishable 6 letter words can be formed in the word CANADA?

Answer 1

The word "Canada" consists of 6 letters, with the letters A appearing 3 times, and the letters C, N, and D appearing once each. To find the number of distinguishable 6-letter words, we can use the formula for permutations of multiset:

[ \frac{n!}{n_1! \times n_2! \times n_3! \ldots} ]

Here, ( n = 6 ) (total letters), ( n_1 = 3 ) (for A), and ( n_2 = n_3 = n_4 = 1 ) (for C, N, and D). Thus, the number of distinguishable words is:

[ \frac{6!}{3! \times 1! \times 1! \times 1!} = \frac{720}{6} = 120. ]

So, there are 120 distinguishable 6-letter words that can be formed from "CANADA."