Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1 – Tn = 10, then the value of n isMaths Questions, Permutation & Combination Questions / By mathemerize Solution : Given, Tn = nC3 Tn+1 = n+1C3 ∴ Tn+1 – Tn = n+1C3 – nC3 = 10 [given] ∴ nC2 + nC3 – nC3 = 10 ⟹ nC2 = 10 ∴ n = 5 Similar Questions How many different words can be formed by jumbling the letters in the word ‘MISSISSIPPI’ in which no two S are adjacent ? From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then In how many ways can 5 different mangoes, 4 different oranges & 3 different apples be distributed among 3 children such that each gets atleast one mango? From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that selection contains one of each category is