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- Question 1 and 2 Exercise 6.1
- Question 3 & 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 1 and 2 Exercise 6.2
- Question 3 and 4 Exercise 6.2
- Question 5 and 6 Exercise 6.2
- Question 7 and 8 Exercise 6.2
- Question 9 Exercise 6.2
- Question 10 Exercise 6.2
- Question 11 Exercise 6.2
- Question 12 Exercise 6.2
- Question 13 Exercise 6.2
- Question 14 and 15 Exercise 6.2
- Question 1 Exercise 6.3
- Question 2 Exercise 6.3
- Question 3 Exercise 6.3
- Question 4 Exercise 6.3
- Question 5 and 6 Exercise 6.3
- Question 7 and 8 Exercise 6.3
- Question 9 Exercise 6.3
- Question 9 Exercise 6.3
- Question 1 Exercise 6.4
- Question 2 Exercise 6.4
- Question 3 Exercise 6.4
- Question 4 Exercise 6.4
- Question 5 Exercise 6.4
- Question 6 Exercise 6.4
- Question 7 Exercise 6.4
- Question 1 and 2 Exercise 6.5
- Question 3 and 4 Exercise 6.5
- Question 5 and 6 Exercise 6.5
- Question 7 Exercise 6.5
- Question 8 Exercise 6.5
- Question 9 Exercise 6.5
- Question 10 Exercise 6.5
- Question 1 Review Exercise 6
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- Question 3 & 4 Review Exercise 6
- Question 5 & 6 Review Exercise 6
- Question 7 & 8 Review Exercise 6
- Question 9 & 10 Review Exercise 6
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Fulltext results:
- Question 3 Exercise 6.4
- ====== Question 3 Exercise 6.4 ====== Solutions of Question 3 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(a)===== A true or false test contains eight questions. If a student guesses the answer for each question, find the probability that $8$ answers are correc
- Question 7 Exercise 6.4
- ====== Question 7 Exercise 6.4 ====== Solutions of Question 7 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Two dice are thrown simultaneously. Fin... c{n(A)}{n(S)}=\dfrac{3}{36}=\dfrac{1}{12}$$ =====Question 7(ii)===== Two dice are thrown simultaneously. Fi
- Question 1 and 2 Exercise 6.1
- ====== Question 1 and 2 Exercise 6.1 ====== Solutions of Question 1 and 2 of Exercise 6.1 of Unit 06: Permutation, Combinat... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Evaluate the $\dfrac{10 !}{3 ! .3 ! \cd... 10.9 .8 .7 .5}{3.2 .1}\\ &=4200 \end{align} =====Question 1(ii)===== Evaluate the $\dfrac{3 !+4 !}{5 !-4 !}
- Question 13 Exercise 6.2
- ====== Question 13 Exercise 6.2 ====== Solutions of Question 13 of Exercise 6.2 of Unit 06: Permutation, Combination and Pr... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 13(i)===== Find the number of permutation of word... \cdot 2 ! \cdot 2 !}\\ &=15,120 \end{align} =====Question 13(ii)===== Find the number of permutation of wor
- Question 4 Exercise 6.4
- ====== Question 4 Exercise 6.4 ====== Solutions of Question 4 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4(i)===== Three unbiased coins are tossed. What i... is: $P(A)=\dfrac{n(A)}{n(S)}=\dfrac{1}{8}$. =====Question 4(ii)===== Three unbiased coins are tossed. What
- Question 1 and 2 Exercise 6.2
- ====== Question 1 and 2 Exercise 6.2 ====== Solutions of Question 1 and 2 of Exercise 6.2 of Unit 06: Permutation, Combinat... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Evaluate $^6 P_6$ ====Solution==== \beg... \dfrac{6 !}{(6-6) !}\\ &=6 !=720\end{align} =====Question 1(ii)===== Evaluate $^{20} P_2$ ====Solution====
- Question 5 and 6 Exercise 6.3
- ====== Question 5 and 6 Exercise 6.3 ====== Solutions of Question 5 and 6 of Exercise 6.3 of Unit 06: Permutation, Combinat... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== How many straight lines are determined ... e, so that gives ${ }^{12} C_2=66$ lines. The question now is whether we have counted any line twice. t
- Question 3 & 4 Exercise 6.1
- ====== Question 3 & 4 Exercise 6.1 ====== Solutions of Question 3 & 4 of Exercise 6.1 of Unit 06: Permutation, Combination ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== Prove that $\dfrac{1}{6 !}+\dfrac{2}{7 ... 6+16+3}{8 !}\\ &=\dfrac{75}{8 !}\end{align} =====Question 3(ii)===== Prove that $\dfrac{(n+5) !}{(n+3) !}=n
- Question 12 Exercise 6.2
- ====== Question 12 Exercise 6.2 ====== Solutions of Question 12 of Exercise 6.2 of Unit 06: Permutation, Combination and Pr... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 12(i)===== How many different word can be formed ... dot 4 \cdot 3 !}{3 !}\\ &=6,720 \end{align} =====Question 12(ii)===== How many different word can be formed
- Question 1 Exercise 6.4
- ====== Question 1 Exercise 6.4 ====== Solutions of Question 1 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(a)===== Let $S=\{1,2,3,4,5,6\}$ be the sample s... ac{n(A)}{n(S)}\\ &=\dfrac{1}{6} \end{align} =====Question 1(b)===== Let $S=\{1,2,3,4,5,6\}$ be the sample s
- Question 6 Exercise 6.4
- ====== Question 6 Exercise 6.4 ====== Solutions of Question 6 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 6(i)===== If one card is drawn at random from a w... e card is: $$=\dfrac{4}{52}=\dfrac{1}{13}$$ =====Question 6(ii)===== If one card is drawn at random from a
- Question 9 Exercise 6.5
- ====== Question 9 Exercise 6.5 ====== Solutions of Question 9 of Exercise 6.5 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9(i)===== A'jmal and Bushra appear in an intervie... times \dfrac{1}{5}=\dfrac{1}{35}\end{align} =====Question 9(ii)===== A'jmal and Bushra appear in an intervi
- Question 7 & 8 Review Exercise 6
- ====== Question 7 & 8 Review Exercise 6 ====== Solutions of Question 7 & 8 of Review Exercise 6 of Unit 06: Permutation, Co... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== If $P(A)=0.8, P(B)=0.5$ and $P(B / A)=0... dot P(A)\\ &=0.4 \times 0.8=0.32\end{align} =====Question 7(ii)===== If $P(A)=0.8, P(B)=0.5$ and $P(B / A)=
- Question 3 and 4 Exercise 6.2
- ====== Question 3 and 4 Exercise 6.2 ====== Solutions of Question 3 and 4 of Exercise 6.2 of Unit 06: Permutation, Combinat... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== Prove by Fundamental principle of count... =\dfrac{n !}{(n-r) !}\\ &=^n P_r\end{align} =====Question 3(ii)===== Prove by Fundamental principle of coun
- Question 7 and 8 Exercise 6.2
- ====== Question 7 and 8 Exercise 6.2 ====== Solutions of Question 7 and 8 of Exercise 6.2 of Unit 06: Permutation, Combinat... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== How many three digits numbers can be fo... $m_1 \cdot m_2 \cdot m_3=5.5 \cdot 5=125$$ =====Question 7(ii)===== How many three digits numbers can be f