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- Question 4 Exercise 6.4
- space of the given problem is: \begin{align}S&=(HHII,HHT.HTH.HTT.THII.THT.TTH,TT7),\\ \text{then} n(S)&=2^3=8\end{align} When all heads. Let $$A=\{H H H\... dfrac{n(A)}{n(S)}=\dfrac{1}{8}$. =====Question 4(ii)===== Three unbiased coins are tossed. What is th... space of the given problem is: \begin{align}S&=(HHII,HHT.HTH.HTT.THII.THT.TTH,TT7),\\ \text{then} n(S
- Question 1 and 2 Exercise 6.1
- .5}{3.2 .1}\\ &=4200 \end{align} =====Question 1(ii)===== Evaluate the $\dfrac{3 !+4 !}{5 !-4 !}$ ===... )}\\ &=\dfrac{5}{16} \end{align} =====Question 1(iii)===== Evaluate the $\dfrac{(n-1) !}{(n+1) !}$ ==... =\dfrac{19 !}{13 !} \end{align} =====Question 2(ii)===== Write $2.4.6 .8 .10 .12$ in term of factori... t 6\\ &=2^6 \cdot 6 !\end{align} =====Question 2(iii)===== Write $n(n^2-1)$ in term of factorial. ===
- Question 1 and 2 Exercise 6.2
- {(6-6) !}\\ &=6 !=720\end{align} =====Question 1(ii)===== Evaluate $^{20} P_2$ ====Solution==== \begi... }\\ &=20 \times 19=380\end{align} =====Question 1(iii)===== Evaluate $^{16} P_3$ ====Solution==== \beg... can not be negative, so $n=11$. =====Question 2(ii)===== Solve $^n P_5=9(^{n-1} P_4)$ for $n.$ ====S... \\ \Rightarrow n&=9 \end{align} =====Question 2(iii)===== Solve $n^2 P_2=600$ for $n$ ====Solution==
- Question 7 Exercise 6.4
- )}=\dfrac{3}{36}=\dfrac{1}{12}$$ =====Question 7(ii)===== Two dice are thrown simultaneously. Find th... }=\dfrac{10}{36}=\dfrac{5}{18}$$ =====Question 7(iii)===== Two dice are thrown simultaneously. Find t... }=\dfrac{4}{36}=\dfrac{1}{9}$$ =====Question 7(vii)===== Two dice are thrown simultaneously. Find th... }=\dfrac{18}{36}=\dfrac{1}{2}$$ =====Question 7(viii)===== Two dice are thrown simultaneously. Find t
- Question 1 Review Exercise 6
- id="a1" collapsed="true">(a): $2520$</collapse> ii. How many two digits odd numbers can be formed fo... e id="a2" collapsed="true">(c): $28$ </collapse> iii. How many six digits number can be formed from t... id="a6" collapsed="true">(d): $4775$</collapse> vii. The number of all possible matrices of order $3 ... id="a7" collapsed="true">(c): $512$</collapse> viii. How many diagonals can be drawn in plane figure
- Question 2 Exercise 6.3
- ....(i)\\ &^n C_r=\dfrac{n !}{(n-r) ! r !}=35....(ii)\end{align} Dividing Eq.(i) by Eq.(ii) \begin{align}\dfrac{n !}{(n-r) !} \cdot \dfrac{(n-r) ! r !}{n... xt{or}\quad r &=4\end{align} Putting $r=4$ in Eq.(ii), we get \begin{align} & { }^n C_4=\dfrac{n !}{(n
- Question 3 & 4 Exercise 6.1
- }\\ &=\dfrac{75}{8 !}\end{align} =====Question 3(ii)===== Prove that $\dfrac{(n+5) !}{(n+3) !}=n^2+9 ... not b negative, therefore $n=6$. =====Question 4(ii)===== Find the value of $n$, when $\dfrac{n !}{(n
- Question 12 Exercise 6.2
- 3 !}{3 !}\\ &=6,720 \end{align} =====Question 12(ii)===== How many different word can be formed from ... ot 2 !}\\ &=151,200 \end{align} =====Question 12(iii)===== How many different word can be formed from
- Question 13 Exercise 6.2
- dot 2 !}\\ &=15,120 \end{align} =====Question 13(ii)===== Find the number of permutation of word "Exc... 2 ! .1 !}\\ &=3360 \end{align} =====Question 13(iii)===== Find the number of permutation of word "Ex
- Question 1 Exercise 6.3
- gative therefore, we have $n=9$. =====Question 1(ii)===== Solve $^{n+1} C_4=6,^{n-1} C_2$ for $n$. ==... ative, therefore we have $n=8$. =====Question 1(iii)===== Solve $n^2 C_2=30 .{ }^n C_3$ for $n$. ===
- Question 9 Exercise 6.3
- 6 !}{(6-4)}\\\ &= 525\end{align} =====Question 9(ii)===== An $8$-persons committee is to be formed fr... : $$21+210+525+420+105+6=1,287$$ =====Question 9(iii)===== An $8$-persons committee is to be formed f
- Question 6 Exercise 6.4
- $$=\dfrac{4}{52}=\dfrac{1}{13}$$ =====Question 6(ii)===== If one card is drawn at random from a well ... }{4}=\dfrac{2}{4}=\dfrac{1}{2}$$ =====Question 6(iii)===== If one card is drawn at random from a well
- Question 9 Exercise 6.5
- c{1}{5}=\dfrac{1}{35}\end{align} =====Question 9(ii)===== A'jmal and Bushra appear in an interview fo... 10}{35}=\dfrac{2}{7} \end{align} =====Question 9(iii)===== A'jmal and Bushra appear in an interview f
- Question 7 & 8 Review Exercise 6
- &=0.4 \times 0.8=0.32\end{align} =====Question 7(ii)===== If $P(A)=0.8, P(B)=0.5$ and $P(B / A)=0.4$,... }{P(B)}=\dfrac{0.32}{0.5}=0.64$$ =====Question 7(iii)===== If $P(A)=0.8, P(B)=0.5$ and $P(B / A)=0.4$
- 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