Course Code
stt211


Question
Four digits numbers are to be formed using any of the digits 1, 2, 3, 4, 5, 6, (No repetition of digit is allowed). How many four digit number can be formed

Answer
360



Question
Ten points are marked on a straight line and 11 points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?

Answer
1045



Question
For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is

Answer
3



Question
An intelligence agency forms a code of two distinct digits selected from 0, 1, 2… 9 such that the first digit of the code is non zero. The code, handwritten on the slip, can create confusion, when read upside down for example the code 91 can be read as 16. How many codes are there for which no such confusion can arise?

Answer
69



Question
Each of the 11 letters A. H, I, M, O, T, U, V, W, X and Z appears same hen looked at in the mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed using only the symmetric letters (no repetition allowed)

Answer
7920



Question
A five digit number is formed using digits 1, 3, 5, 7 and 9without repeating any one of them. What is the sum of all such possible numbers?

Answer
6666600



Question
The number of partitions of {1, 2, 3, 4, 5} into three blocks is S(5, 3) = 25. The total number of functions f : {1, 2, 3, 4, 5} ! {1, 2, 3, 4} with |Image(f)| = 3 is

Answer
\(4\times 25\times 6\)



Question
Let f : {1, 2, 3, 4, 5, 6, 7, 8, 9} ! {a, b, c, d, e}. In one-line notation, f = (e, a, b, b, a, c, c, a, c) (use number order on the domain). Which is correct?

Answer
Image(f) = {a, b, c, e}, Coimage(f) = {{6, 7, 9}, {2, 5, 8}, {3, 4}, {1}}



Question
Let S = 452631 be a permutation on {1, 2, 3, 4, 5, 6} in one-line notation (based on the usual order on integers). Which of the following is NOT a correct cycle notation for S?

Answer
(461) (352)



Question
Let \(A = {0, 1} \times {0, 1}\) and B = {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is in alphabetic order. If \(A \times B\times A\) is listed in lexicographic order, then the next element after ((1, 0), c, (1, 1)) is

Answer
((1, 1), a, (0, 0))


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