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- Question 2 Exercise 6.3
- ....(i)\\ &^n C_r=\dfrac{n !}{(n-r) ! r !}=35....(ii)\end{align} Dividing Eq.(i) by Eq.(ii) \begin{align}\dfrac{n !}{(n-r) !} \cdot \dfrac{(n-r) ! r !}{n... xt{or}\quad r &=4\end{align} Putting $r=4$ in Eq.(ii), we get \begin{align} & { }^n C_4=\dfrac{n !}{(n
- Question 1 and 2 Exercise 6.1
- .5}{3.2 .1}\\ &=4200 \end{align} =====Question 1(ii)===== Evaluate the $\dfrac{3 !+4 !}{5 !-4 !}$ ===... =\dfrac{19 !}{13 !} \end{align} =====Question 2(ii)===== Write $2.4.6 .8 .10 .12$ in term of factori
- Question 3 & 4 Exercise 6.1
- }\\ &=\dfrac{75}{8 !}\end{align} =====Question 3(ii)===== Prove that $\dfrac{(n+5) !}{(n+3) !}=n^2+9 ... not b negative, therefore $n=6$. =====Question 4(ii)===== Find the value of $n$, when $\dfrac{n !}{(n
- Question 1 and 2 Exercise 6.2
- {(6-6) !}\\ &=6 !=720\end{align} =====Question 1(ii)===== Evaluate $^{20} P_2$ ====Solution==== \begi... can not be negative, so $n=11$. =====Question 2(ii)===== Solve $^n P_5=9(^{n-1} P_4)$ for $n.$ ====S
- Question 5 Exercise 6.1
- .3 .5 \ldots(2 n-1))\end{align} =====Question 5(ii)===== Show that: $\dfrac{(2 n+1) !}{n !}=2^n(1.3
- Question 3 and 4 Exercise 6.2
- }{(n-r) !}\\ &=^n P_r\end{align} =====Question 3(ii)===== Prove by Fundamental principle of counting
- Question 7 and 8 Exercise 6.2
- m_2 \cdot m_3=5.5 \cdot 5=125$$ =====Question 7(ii)===== How many three digits numbers can be formed
- Question 10 Exercise 6.2
- .3 !}{3 !}\\ &=1680\end{align} =====Question 10(ii)===== In how many ways can five students be seate
- Question 11 Exercise 6.2
- d less than $100$ are: $$m_1 \cdot m_2=5.5=25$$ (ii) Numbers greater than $100$ and less than $1000$
- Question 12 Exercise 6.2
- 3 !}{3 !}\\ &=6,720 \end{align} =====Question 12(ii)===== How many different word can be formed from
- Question 13 Exercise 6.2
- dot 2 !}\\ &=15,120 \end{align} =====Question 13(ii)===== Find the number of permutation of word "Exc
- Question 1 Exercise 6.3
- gative therefore, we have $n=9$. =====Question 1(ii)===== Solve $^{n+1} C_4=6,^{n-1} C_2$ for $n$. ==
- Question 4 Exercise 6.3
- H} \cdot \mathrm{S}\end{align} =====Question 4(ii)===== Prove that: $r \cdot{ }^n C_r=n^{n-1} C_{r-
- Question 5 and 6 Exercise 6.3
- of the given points on any line. =====Question 5(ii)===== How many triangles are determined by $12$ p
- Question 9 Exercise 6.3
- 6 !}{(6-4)}\\\ &= 525\end{align} =====Question 9(ii)===== An $8$-persons committee is to be formed fr