Q36 / 110 · VITEEE 2024 · Mathematics

If 6 letter words, with or without meaning can be formed out of these letters of the word "MATHEMATICS", repetition of letters is not allowed is $960 P$. Then, ' $P$ ' equals

  • A
    18
  • B
    20
  • Correct answer
    C
    21
  • D
    23

Solution

Unique letters in the word "MATHEMATICS" is $=8(M, A, T, H, E, I, C, S)$ Total ways of selecting 6 letters out of 8 unique letters $={ }^8 C_6=28$ and total arrangements of 6 selected letters $=6!=720$ Therefore, total numbers of 6 letters word $=720 \times 28=20160$ According to the question, $960 P=20160 \Rightarrow P=\frac{20160}{960}=21$

Hence, the correct answer is option: 'C'.

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