Combination
Q21.
The number of substrings (of all lengths inclusive) that can be formed from a character string of length n isQ22.
Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?Q23.
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from same suit isQ24.
How many sub strings of different lengths (non-zero) can be formed from a character string of length n?Q25.
Let \Sigma = (a, b, c, d, e) be an alphabet. We define an encoding scheme as follows : g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11. Let p_{i} denote the i-th prime number (p_{i}=2). For a non-empty string s=a_{1}...a_{n}, where each a_{i} \in \Sigma, define f(i)=\prod_{i=1}^{n}{P_{i}}^{g(a_{i})}. For a non-empty sequence < s_{j},...,s_{n} > of strings from \Sigma^{+}, define h(<s_{i}...s_{n} >)=\prod_{i=1}^{n}{P_{i}}^{f(s_{i})} Which of the following numbers is the encoding, h, of a non-empty sequence of strings?Q26.
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of k colours, such that he colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of k that satisfies this requirement?Q27.
In how many ways can we distribute 5 distinct balls, B_1, B_2, \ldots, B_5 in 5 distinct cells, C_1, C_2, \ldots, C_5 such that Ball B_i is not in cell C_i, \forall i= 1,2,\ldots 5 and each cell contains exactly one ball?