Discussion
What is the total number of distinct ways in which the toddler can place the cards ?
Answer: C
The number of ways is 6! / 2.
MIDDLE has 6 letters, with D appearing twice. Arrangements of 6 cards are 6!, but swapping the two identical D cards gives the same visible arrangement, so each is counted twice:
\[ \frac{6!}{2!} = \frac{720}{2} = 360 \]
6! would treat the two Ds as different, 5! fixes one card, and 6! - 4! has no basis.
In general, n objects with one item repeated r times can be arranged in \(\frac{n!}{r!}\) distinct ways.
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