From a month of 31 days, 3 different dates ar | vedclass

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

Question

(NONE) Total ways to select $3$ distinct dates from $31$ is $\binom{31}{3} = \frac{31 	imes 30 	imes 29}{3 	imes 2 	imes 1} = 4495$.Let the dates

Vedclass · Accepted Answer

$127$

Vedclass · Answer

(NONE) Total ways to select $3$ distinct dates from $31$ is $\binom{31}{3} = \frac{31 	imes 30 	imes 29}{3 	imes 2 	imes 1} = 4495$.Let the dates be $d_1, d_2, d_3$ such that $1 \le d_1 The conditions are $d_1 \ge 1$ and $d_3 \le 31$.Substituting, $a-d \ge 1 \implies a \ge d+1$ and $a+d \le 31 \implies a \le 31-d$.For a fixed $d$, the number of possible values for $a$ is $(31-d) - (d+1) + 1 = 31-2d$.Since $a$ must exist, $31-2d \ge 1 \implies 2d \le 30 \implies d \le 15$.The total number of such $A$.$P$.s is $\sum_{d=1}^{15} (31-2d) = 29 + 27 + 25 + ... + 1$.This is an arithmetic series with $15$ terms, sum $= \frac{15}{2}(29+1) = 15 	imes 15 = 225$.Probability $= \frac{225}{4495} = \frac{45}{899}$.Here $a = 45, b = 899$. Since $	ext{gcd}(45, 899) = 1$, $a+b = 45 + 899 = 944$.

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

Similar Questions

If the probability that a randomly chosen $6$-digit number formed by using digits $1$ and $8$ only is a multiple of $21$ is $p$,then $96p$ is equal to

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6\}$. If the probability of this equation having two distinct real roots is $p$,then $216p$ equals:

If $3$ dice are thrown, the probability of getting $10$ as the sum of the three numbers that appeared on the top faces of the dice is

If six students,including two particular students $A$ and $B,$ stand in a row,then the probability that $A$ and $B$ are separated with one student in between them is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

Vedclass Test Series

Exam Paper Generator

Online Exam Module