class 11

Math

Algebra

Permutations and Combinations

Let $T_{n}$be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1}−T_{n}=10$, then the value of n is

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The number of ways, in which 12 identical coins can be put into 5 different purses, if none of the purses remain empty, is

The number of ways in which the letters of the word $_{′′}STRANGE_{′′}$ can be arranged so that the vowels may appear in the odd place, is

How many words can be formed from the letters of the word 'DAUGHTER' so that the vowels always come together?

Number of permutations of the letters of the word $_{′}MESMERISE_{′}$ is

Three digit numbers in which the middle one is a perfect square are formed using the digits $1$ to $9$. Their sum is

Let $X$ be a set containing n elements. Two subsets $A$ and $B$ of $X$ are chosen at random, the probability that $A∪B=X$ is

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw

Number of quadrilaterals that can be constructed from the vertices of a decagon (10 Sided polygons) such that none of the sides of the quadrilaterals is also a side of the decagon, is ?