There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?

Question

Option 1: 3388

Option 2: 3376

Option 3: 3366

Option 4: 3327

AfterBoards · Accepted Answer

For Beetles: Can select from 12 identical copies, ranging from selecting 1 to 12 copies Ways = 12 choices (like selecting from a box with repetition allowed) For Pink Floyd: Can select from 7 identical copies, ranging from selecting 1 to 7 copies Ways = 7 choices For Michael Jackson: Have 3 different CDs Can select any combination of these 3 Ways = 2^3 - 1 = 7 (excluding selecting none) For Madonna: Have 2 different CDs Ways = 2^2 - 1 = 3 (excluding selecting none) Total possible ways using multiplication principle for independent events, where we can select from any combination of artists: = (12 + 1)(7 + 1)(7 + 1)(3 + 1) - 1 = 13 × 8 × 8 × 4 - 1 = 3328 - 1 = 3327 We add 1 to each artist's selections to include the option of not selecting from that artist, multiply all options together to get all possible combinations, and subtract 1 at the end to exclude the case where nothing is selected at all.

IPMAT Rohtak 2020 (QA) PYQs

There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?

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