The number of seven-digit integers with the s | vedclass

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

Question

(C) Let the seven digits be $x_1, x_2, x_3, x_4, x_5, x_6, x_7$ such that $x_i \in \{1, 2, 3\}$ and $\sum_{i=1}^{7} x_i = 10$.Case $I$: The digits are

Vedclass · Accepted Answer

$77$

Vedclass · Answer

(C) Let the seven digits be $x_1, x_2, x_3, x_4, x_5, x_6, x_7$ such that $x_i \in \{1, 2, 3\}$ and $\sum_{i=1}^{7} x_i = 10$.Case $I$: The digits are $1, 1, 1, 1, 1, 2, 3$.Sum $= 1+1+1+1+1+2+3 = 10$.The number of arrangements is $\frac{7!}{5!1!1!} = \frac{7 	imes 6}{1} = 42$.Case $II$: The digits are $1, 1, 1, 1, 2, 2, 2$.Sum $= 1+1+1+1+2+2+2 = 10$.The number of arrangements is $\frac{7!}{4!3!} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.Total number of such integers $= 42 + 35 = 77$.

The number of seven-digit integers with the sum of the digits equal to $10$ and formed by using the digits $1, 2,$ and $3$ only is:

Similar Questions

The total number of three-digit and five-digit integers which can be formed by using the digits $0, 1, 2, 3, 4, 5$,using each digit not more than once in each number,is:

The number of positive integral solutions of $abc = 30$ is

If all the letters of the word $COMBINATION$ are arranged in all possible ways to form $11$ letter words (with or without meaning),then the number of words among them in which $C$ and $N$ occupy the end positions and no vowel appears exactly in the middle position is

The number of ways in which we can select three numbers from $1$ to $30$ such that we exclude every selection consisting of all even numbers is

The number of distinct primes dividing $12! + 13! + 14!$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module