Multiple choice

There are a total of 11 things out of which 4 are alike of one kind , 3 are alike of another kind and the rest are different . Then the total number of ways in which a selection of atleast one thing can be made from them is

  1. 192

  2. 319

  3. 318

  4. None of these
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B Correct answer
Explanation

Total items = 11. 4 alike of one kind, 3 alike of another, 4 different. Number of ways to select at least one = (4+1)(3+1)(2^4) - 1 = 5 * 4 * 16 - 1 = 320 - 1 = 319.

AI explanation

Using the method of selection for grouped objects, the 4 identical items offer 5 choices and the 3 identical items offer 4 choices. The 4 distinct items offer 2 to the power of 4, or 16, choices. The total combinations are 5 times 4 times 16, giving 320, from which 1 is subtracted to exclude selecting nothing. The result is 319.

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