Exercise 7. Find the number of bit strings of length 15 that have exactly three

Question

Exercise 7. Find the number of bit strings of length 15 that have exactly three 1s Exercise 8. The goal of this exercise is to find the number of integer solutions of the equation xitx2 +"3 +24 = 12 such that zi 2 0, i = 1, 2, 3 and 4. Suppose that you have 12 marbles to place in 4 boxes (z? is the number of marbles put in box 1, x2 is the number of marbles put in box 2,..). One way to do this is, as shown in the picture, x -1,r2-3, 4 and x-4 Now, if we denote the marbles of the picture by zeros delimited by ones in a bit string of length 15, we get 0 1 000 1 0000 1 0000 Use your solution of Exercise 7 to solve the equation x1 + x2 +x3 + z4 = 12 where xi E NU {0}

Explanation / Answer

7.

The number of bit strings of length 15 that has exactly 3 1s

= 15C3 = 455

The number of bit strings of length 15 that has exactly 3 1s = 455

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