Multiple choice

Seven distinct academic prizes are to be given to some students from a class of 50 students. Four prizes out of these are to be given to 4 distinct students. The rest three prizes can be given to any student even if he has won any other prize before. In how many ways can this be done?

  1. 50C4 × (50)3

  2. 50C4 + (50)3

  3. 50C4 × (3)50

  4. 50C4 + (3)50

  5. None of these
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A Correct answer
AI explanation

Using the method of combinations for independent choices, we first select the four students for the four distinct prizes, which can be done in 50C4 ways. Since the remaining three prizes can be awarded to any of the 50 students regardless of previous wins, there are 50 choices for each of the three prizes, giving 50 multiplied by 50 multiplied by 50 ways. Multiplying these independent results gives the total number of ways as 50C4 multiplied by (50) cubed.

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