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- Question 9 Exercise 6.3
- Question 9(i)===== An $8$-persons committee is to be formed from a group of $6$ women and $7$ men. In how many ways can the committee be chosen if (i) committee must contain four men and... Total number of different ways that four men to be selected are: ${ }^7 C_4$. Total number of different ways that four women to be selected are ${ }^6 C_4$. By fundamental princip
- Question 7 and 8 Exercise 6.2
- stion 7(i)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if repetit... hundred digit, ten digit and unit digit place) to be filled by five digits, Moreover repetition is a... tion 7(ii)===== How many three digits numbers can be formed from the digits $1,2,3,4$ and 5 if repetit... estion 8===== How many different arrangements can be formed of the word "equation" if all the vowels a
- Question 9 Exercise 6.5
- respectively. Find the probability that both will be selected. ====Solution==== \begin{align} P(\text ... ected In this case there are two chance. it may be Ajmal selected Bushra not selected that is $P(A \cap \bar{B})$. The second option is it may be Bushra selected but Ajmal not that is $P(\bar{A} ... respectively. Find the probability that none will be sclected. ====Solution==== \begin{align} P(\text
- Question 1 Review Exercise 6
- ollapse> ii. How many two digits odd numbers can be formed form the digits $\{1,2,3,4,5,6,7\}$ if rep... </collapse> iii. How many six digits number can be formed from the digits $\{1,2,3,4,6,7,8\}$ withou... e> v. In how many different ways can $5$ couples be seated around a circular table if the couple must not be separated? * (a) $768$ * %%(b)%% $724
- Question 10 Exercise 6.2
- ion 10(i)===== In how many ways can five students be seated in a row of eight seals if a certain two s... The total number of ways these five students can be seated are: \begin{align}^8 P_5&=\dfrac{8 !}{(8-5... t next to each other then these two students will be handled as a single students and the eights seats will be considered as 7. In this case the total number o
- Question 1 Exercise 6.4
- =====Question 1(a)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(b)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(c)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p... =====Question 1(d)===== Let $S=\{1,2,3,4,5,6\}$ be the sample space of rolling a dice. What is the p
- Question 9 & 10 Review Exercise 6
- ===== How many numbers greater than a million can be formed with the digits $2,3,0,3,4,2,3$? ====Solut... otal numbers that do not start with zero. It can be formed using the given $7$ digits taking out $0$ ... . =====Question 10===== A party of $n$ men is to be seated around a circular table. Find the probabil... === The total number of ways that $n$ persons can be seated around a circular table are: $(n-1)$ ! If
- Question 5 and 6 Exercise 6.2
- In how many ways can letter of the word 'Fasting' be arranged? ====Solution==== The total number of al... ==Question 6===== How many four digits number can be formed from the digits $2,4,5,7,9$ ? (Repetition ... gits are: $$=5.4 .3 .2=120\quad \text{or}$$ can be found using permutation as: $$^5 P_4=\dfrac{5 !}{... f these for even number, the unit digit have to be filled by $2$ or $4$. So, we are left with $3$ nu
- Question 12 Exercise 6.2
- ==Question 12(i)===== How many different word can be formed from the letters "BOOKWORM" if the letters... =Question 12(ii)===== How many different word can be formed from the letters "BOOKKEEPER" if the lette... Question 12(iii)===== How many different word can be formed from the letters "ABBOTTABAD" if the lette... =Question 12(iv)===== How many different word can be formed from the letters "LETTER" if the letters a
- Question 14 and 15 Exercise 6.2
- =Question 15===== In how many ways can $7$ people be arranged at a round table so that 2 particular pe... ution==== Nurnber of ways in which $7$ people can be seated around a round table without any condition... one unit. Number of ways in which $6$ people can be arranged around a round table is $5!$ And the two particular people can be arranged between them selves in $2 !=2$ ways. He
- Question 1 and 2 Exercise 6.2
- 1& \text{or}\quad n=-4\end{align} But $n$ can not be negative, so $n=11$. =====Question 2(ii)===== So... or}\quad n&=\sqrt{24}i\end{align} but $n$ can not be negative nor it can be imaginary, therefore, $n=5$. ====Go To==== <text align="right"><btn type
- Question 3 Exercise 6.4
- his event, because we can select all question to be correct by one way i.e. $${ }^8 C_8=\dfrac{8 !}{... re correct. Let $$D=\{6\}$$ Here $6$ question to be correct are at least maximum may be eight correct. so the possible oulcome in this case \begin{align
- Question 10 Exercise 6.5
- th are apples or both are non defective: Let $E$ be the event that either both are apples or both are non defective. $a A$ be the event that both are apples. $B$ be the event that both are non defective. Total number of ways
- Question 5 & 6 Review Exercise 6
- Question 5(i)===== In how many different ways can be six children seated at a round table if certain t... uestion 5(ii)===== In how many different ways can be six children seated at a round table if certain t... ==== Six people including Faisal and Saima are to be seated at a round circular table. Find the probab
- Question 11 Exercise 6.2
- ny numbers each lying between $10$ and $1000$ can be formed with digits $2.3,4,0,8,9$ using only once?... t of three digits but hundred digit place can not be occupy by the digit $0$ \\ Hundred digit: Event $