Unformatted text preview: 16-2. Problem 2. For each integer between 1 and 15 we have 2 choices: we can put it in box 1 or in box 2. Since box 1 has exactly ﬁve integers we must use box 1 ﬁve times and so, we must use box 2 ten times. So we are really arranging ﬁve 1s and ten 2s in row. The requirement that consecutive integers cannot go into box 1 means that there are no consecutive 1s in the arrangement. So let us ﬁrst arrange the ﬁve 1s: 1 1 1 1 1 Now we want to distribute the 2s making sure that there are no consecutive 1s. So ﬁrst put a 2 into each of the 4 spaces between the 1s. Now, we are left with 6 2s to distribute into the 6 spaces. So there are ³ 6 + 6-1 6 ! ways to do this. 1...
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- Spring '11
- Natural number, Dilip Raghavan