Let S denote the set of 4-digit numbers abcd | vedclass

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

Question

(B) For $n(S)$, we need to choose $4$ distinct digits from the set ${0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$. Since the condition $a > b > c > d$ is given, onc

Vedclass · Accepted Answer

$260$

Vedclass · Answer

(B) For $n(S)$, we need to choose $4$ distinct digits from the set ${0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$. Since the condition $a > b > c > d$ is given, once $4$ digits are chosen, there is only $1$ way to arrange them in descending order. Thus, $n(S) = {}^{10}C_4 = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} = 210$. For $n(P)$, we need $5$-digit numbers whose product of digits is $20$. The prime factorization of $20$ is $2^2 	imes 5$. The possible sets of $5$ digits are: $1)$ ${5, 4, 1, 1, 1}$: The number of arrangements is $\frac{5!}{3!} = 20$. $2)$ ${5, 2, 2, 1, 1}$: The number of arrangements is $\frac{5!}{2!2!} = 30$. Thus, $n(P) = 20 + 30 = 50$. Therefore, $n(S) + n(P) = 210 + 50 = 260$.

Let $S$ denote the set of $4$-digit numbers $abcd$ such that $a > b > c > d$ and $P$ denote the set of $5$-digit numbers having the product of its digits equal to $20$. Then $n(S) + n(P)$ is equal to:

Similar Questions

The number of triplets $(x, y, z)$,where $x, y, z$ are distinct non-negative integers satisfying $x+y+z=15$,is

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,is

The total number of $3$-digit numbers,whose greatest common divisor with $36$ is $2$,is

$A$ set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module