Combination


Q21.

The number of substrings (of all lengths inclusive) that can be formed from a character string of length n is
GateOverflow

Q22.

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?
GateOverflow

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 is
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Q24.

How many sub strings of different lengths (non-zero) can be formed from a character string of length n?
GateOverflow

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?
GateOverflow

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?
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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?
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