Q58 / 160 · TS EAMCET 2024 (09 May Shift 1) · Mathematics

The number of all possible combinations of 4 letters which are taken from the letters of the word ACCOMMODATION is

  • Correct answer
    A
    167
  • B
    161
  • C
    160
  • D
    157

Solution

$A-2, C-2, O-3, M-2, D-1, T-1, I-1, N-1$ The following cases arise : 3 alike and one different - No. of ways is 7 . 2 alike and 2 alike - No. of ways $={ }^4 C_2=6$ 2 alike, 2 different $={ }^4 C_1 \times{ }^7 C_2=4 \times 21=84$ All 4 different $={ }^8 C_4=70$ Total no. of ways $=167$.

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

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