The number of ways in which an examiner can a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the marks assigned to the $8$ questions be $x_1, x_2, \dots, x_8$. We are given that $x_1 + x_2 + \dots + x_8 = 30$,where $x_i \ge 2$ for all

Vedclass · Accepted Answer

$^{21}C_7$

Vedclass · Answer

(C) Let the marks assigned to the $8$ questions be $x_1, x_2, \dots, x_8$. We are given that $x_1 + x_2 + \dots + x_8 = 30$,where $x_i \ge 2$ for all $i = 1, 2, \dots, 8$. Let $x_i = y_i + 2$,where $y_i \ge 0$. Substituting this into the equation,we get: $(y_1 + 2) + (y_2 + 2) + \dots + (y_8 + 2) = 30$ $y_1 + y_2 + \dots + y_8 + 16 = 30$ $y_1 + y_2 + \dots + y_8 = 14$. The number of non-negative integer solutions to this equation is given by the formula $^{n+r-1}C_{r-1}$,where $n=14$ and $r=8$. Number of ways $= ^{14+8-1}C_{8-1} = ^{21}C_7$.

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

Similar Questions

An examiner can assign $30$ marks to $8$ questions. If he does not assign less than $2$ marks to any question,in how many ways can he assign the marks?

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

If $\binom{n}{3} + \binom{n}{4} > \binom{n+1}{3}$,then:

$A$ bag contains $3$ coins of one rupee,$4$ coins of fifty paise,and $5$ coins of ten paise. If at least one coin is selected from the bag,what is the total number of ways to make the selection?

Vedclass Test Series

Exam Paper Generator

Online Exam Module