Question

From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.

• A. \( \frac{1}{16} \)
• B. \( \frac{3}{8} \)
• C. \( \frac{1}{4} \)
• D. \( \frac{3}{16} \)

Hint:

Permutations of r distinct letters from n: \( {}^nP_r = \frac{n!}{(n-r)!} \)

Answer 1

The Correct Option is D

Letters: C, U, R, V, E (5 distinct letters) Total words with at least 2 letters: \[ \Rightarrow {}^5P_2 + {}^5P_3 + {}^5P_4 + {}^5P_5 = 20 + 60 + 120 + 120 = 320 \] Favorable: 3-letter words: \( {}^5P_3 = 60 \) \[ \text{Required probability } = \frac{60}{320} = \frac{3}{16} \]