# Ch 07: Permutation, Combination and Probability

- Find $n$ when ${^nC_{12}}={^nC_6}$ —
*BISE Gujranwala(2015)* - Evaluate ${^{20}C_{17}}$ without calculator —
*BISE Gujranwala(2015)* - How many $6-digit$ numbers can be formed from the digits $2,2,3,3,4,4$? How many of them with lie between $400,000$ and $430,000$? —
*BISE Gujrawala(2015)* - How many words can be formed from the letter $``PLANE"$ using all letters (no letter is repeated) —
*BISE Gujrawala(2017)* - Prove that $^nC_4=^nC_{n-r}$ —
*BISE Gujrawala(2017)* - Find the numbers of diagonals of a $6-digits$ figures —
*BISE Gujrawala(2017)* - A coin is tossed four times, find the probability that top shows all heads. —
*BISE Gujranwala(2017)* - Show that $n^3-n$ is divisible by $6$ for $n=2,3$ —
*BISE Gujrawala(2017)* - Find the value of $n$ when $^nP_2=30$ —
*BISE Sargodha(2015)* - Find numbers of diagonals of $6-dided$ figure. —
*BISE Sargodha(2015)* - Find the value of $n$. $^nC_{12}=^nC_6$ —
*BISE Sargodha(2015)* - Determine the probability of getting two heads in two successive tosses of a coin? —
*BISE Sargodha(2015)* - Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^nC_r$ —
*BISE Sargodha(2015)* - If $\frac{a_5}{a_3}=\frac{4}{9}$, $a_2=\frac{4}{9}$ in $G.P$. Find $a_n$ —
*BISE Sargodha(2015)* - Find $n$, when $^{11}P_n=11.10.9$—
*BISE Sargodha(2015), BISE Sargodha(2016)* - In how many way can a hockey team of $11$ be selected out of $15$ players. —
*BISE Sargodha(2015)* - A die is thrown. Find the probability that the dots on the top are prime number or odd number. —
*BISE Sargodha(2015)* - The sum of $9$ teams of an $A.P.$ is $171$ and its eighth team is $31$. Find the series. —
*BISE Sargodha(2015)* - Prove that $^nC_r+^nC_{r-1}=^{n+1}C_r$ —
*BISE Sargodha(2015)* - Find the sum of $\frac{9}{4}+\frac{3}{2}+1+\frac{2}{3}+\ldots\infty$ —
*BISE Sargodha(2016)* - Evaluate $^{20}C_{17}$ —
*BISE Sargodha(2016)* - Prove that $^{n-1}C_r+^{n-1}C_{r-1}=^n C_r$ —
*BISE Sargodha(2016)* - Prove that $^nC_r=^nC_{n-r}$ —
*BISE Sargodha(2017)* - In how many ways can $4$ keys be arranged on a circular key ring? —
*BISE Sargodha(2017)* - How many words can be formed from the letters of the word $``objective“$ using all letters without repeating anyone? —
*BISE Lahore(2017)* - Find the values of $n$ and $r$ when $^nC_r=35$ and $^nP_r=210$ —
*FBISE(2016), BISE Lahore(2017)* - If $S=\{1,2,3,\ldots9\}$, Even $A=\{2,4,6,8\}$, $B=\{1,3,5\}$. Find $P(A \cup B)$ —
*BISE Lahore(2017)* - A die is thrown. Find probability that the dots on the top are prime numbers or odd numbers. —
*BISE Lahore(2017)* - Find the values of $n$ and $r$ when $^{n-1}C_{r-1}:^nC_r:^{n+1}C_{r+1}=3:6:10$ —
*FBISE(2017)* - Show that sum of $n$ $AM's$ between $a$ and $b$ is equal to $n$ times their $AM's$ —
*FBISE(2017)*