Question

how many distinct permutations can be formed using the letters of the word \connection\?
there are □ distinct permutations.
(type a whole number.)

Explanation:

Step1: Count total letters

Total letters in "CONNECTION": 10, so $n=10$.

Step2: Count repeated letters

Repeats: C(2), O(2), N(3), E(1), T(1), I(1). So $n_1=2, n_2=2, n_3=3$.

Step3: Apply permutation formula

Use formula for distinct permutations: $\frac{n!}{n_1!n_2!n_3!}$
$$\frac{10!}{2! \times 2! \times 3!}$$

Step4: Calculate factorial values

$10!=3628800$, $2!=2$, $3!=6$

Step5: Compute final value

$$\frac{3628800}{2 \times 2 \times 6} = \frac{3628800}{24} = 151200$$

Answer:

151200