Discussion
How many combinations are possible while selecting four letters from the word ‘SMOKEJACK’ with the condition that ‘J’ must appear in it?
Answer: D
SMOKEJACK has nine letters with K appearing twice. J must be one of the four, so three more are chosen from S, M, O, K, E, A, C - with K available twice.
At most one K - choose 3 of the 7 distinct letters:
\[ {}^{7}C_{3} = 35 \]
Both K's - choose 1 more from the other 6:
\[ {}^{6}C_{1} = 6 \]
\[ 35 + 6 = 41 \]
The repeated K is what makes this more than a plain \( {}^{7}C_{3} \); the two-K selections are genuinely different combinations.
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