nCr ও সম্পূরক সমাবেশ বিষয়ক
12C9 ^{12}C_9\ 12C9 এর মান-
0
220
12
144
12C9 { }_{12} \mathrm{C}_{9} 12C9
=12!9!⋅3!=12⋅11⋅10⋅9!9!⋅3!=12⋅11⋅103!=12⋅11⋅103⋅2⋅1 \begin{array}{l}=\frac{12!}{9!\cdot 3!} \\ =\frac{12 \cdot 11 \cdot 10 \cdot 9!}{9!\cdot 3!} \\ =\frac{12 \cdot 11 \cdot 10}{3!} \\ =\frac{12 \cdot 11 \cdot 10}{3 \cdot 2 \cdot 1}\end{array} =9!⋅3!12!=9!⋅3!12⋅11⋅10⋅9!=3!12⋅11⋅10=3⋅2⋅112⋅11⋅10
=220
If nC3=nC5′\displaystyle ^{n}C_{3}= ^{n}C_{5'}nC3=nC5′ then find the value of n:
C1C0+2C2C1+3C3C2+.....+nCnCn−1=\dfrac { { C }_{ 1 } }{ { C }_{ 0 } } +\dfrac { 2{ C }_{ 2 } }{ { C }_{ 1 } } +\dfrac { { 3C }_{ 3 } }{ { C }_{ 2 } } +.....+\dfrac { { nC }_{ n } }{ { C }_{ n-1 } } =C0C1+C12C2+C23C3+.....+Cn−1nCn=
nPr=54 { }^{n} P_{r}=54 nPr=54 এবং nCr=9 { }^{n} C_{r}=9 nCr=9 হলে, r r r এর মান নির্ণয় কর।
If (1+x)15=C0+C1xC2x2+...+C15x15,(1+x)^{15}=C_{0}+C_{1}xC_{2}x^{2}+...+C_{15}x^{15},(1+x)15=C0+C1xC2x2+...+C15x15, then 15C02−15C12+15C22−15C23+...15C152^{15}C_{0}^{2}- ^{15}C_{1}^{2}+^{15}C_{2}^{2}- ^{15}C_{2}^{3}+... ^{15}C_{15}^{2}15C02−15C12+15C22−15C23+...15C152 is equal to
