Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and Binomial Theorem - 10.2 Exercises - Skill Practice - Page 695: 36

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Row 0: $1$ Row 1: $1+1=2$ Row 2: $1+2+1=4$ Row 3: $1+3+3+1=8$ Row 4: $1+4+6+4+1=16$ Row n: $\sum=_nC_0+_nC_1+_nC_2+nC_3+...+nC_n \\=_nC_01^n1^0+_nC_11^{n-1}1+_nC_21^{n-2}1^2+_nC_11^{n-3}1^3+..._nC_n1^01^n\\=(1+1)^n\\=2^n$