If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
We have $^{n} C _{9}=\,^{n} C _{8}$
i.e., $\frac{n !}{9 !(n-9) !}=\frac{n !}{(n-8) ! 8 !}$
or $\frac{1}{9}=\frac{1}{n-8}$ or $n-8=9$ or $n=17$
Therefore $^{n} C_{17}=\,^{17} C_{17}=1$
Similar Questions
The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is
The number of ways in which we can select three numbers from $1$ to $30$ so as to exclude every selection of all even numbers is
The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is
The number of ways in which $21$ identical apples can be distributed among three children such that each child gets at least $2$ apples, is
- [JEE MAIN 2024]
The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and middle letter is consonant, is
The number of arrangements of the letters of the word $SATAYPAUL$ such that no two $A$ are together and middle letter is consonant, is
If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is
On the occasion of Deepawali festival each student of a class sends greeting cards to the others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is