Class 11

Math

Algebra

Permutations and Combinations

Find the number of ways in which $12$ different flowers can be arranged in a garland so that.

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Statement 1: The number of positive integral solutions of $abc=30$ is 27. Statement 2: Number of ways in which three prizes can be distributed among three persons is $3_{3}$

Find the number of ways in which we can choose 3 squares on a chess board such that one of the squares has its two sides common to other two squares.

The total number of ways of selecting two numbers from the set ${1,2,3,4,……..3n}$ so that their sum is divisible by 3 is equal to a. $22n_{2}−n $ b. $23n_{2}−n $ c. $2n_{2}−n$ d. $3n_{2}−n$

Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.

If all the permutations of the letters in the word OBJECT are arranged (and numbered serially) in alphabetical order as in a dictionary, then the 717th word is a. TOJECB b. TOEJBC c. TOCJEB d. TOJCBE

Number of ways in which Rs. 18 can be distributed amongst four persons such that nobody receives less than Rs. 3 is a. $4_{2}$ b. $2_{4}$ c. $4!$ d. none of these

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order s in an English dictionary. The number of words that appear before the word COCHIN is a.$360$ b. $192$ c. $96$ d. $48$

Let $S={1,2,3,4}$ . The total number of unordered pairs of disjoint subsets of $S$ is equal a.$25$ b. $34$ c. $42$ d. $41$