A Cantabil showroom offers 7 styles of pants. For each style, there are 10 different possible waist sizes, 6 pants lengths and 4 color choices. How many different types of pants could the showroom have?
To find the total number of different types of pants, we multiply the number of choices for each attribute:
7 styles × ______ ___ _________ _________ ________ _______ ___ ______ _____ _______ ___.
_______ ____ _________ ________ _________.
________ ____ ________ _________ ______.
_____ _______ _________ ________ ____ _____ ___ __________ _________ ______ ________ ___.
___ ______ ____ ______ ___ ____ ________ ____ _____ _______ ___ ________.
___ _______ _________ _______ ______.
___ ____ _______ _________ __________ _________ ____ _____ ___ ____ _____ ________.
__________ _______ _________ _________ ____ _________ ___ __________.
___ ____ _____ ________ __________ _________ _________ ___.
______ ________ __________ ___ __________ _____.
_________ _______ _____ _____ _____ _____.
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State whether the following statements are true or false. Justify your answer with a short explanation or a counter-example. (2 × 10 = 20)
(i) The contra- positive of the statement and
is
and
(ii) is the solution of the recurrence relation
(iii) The number of integers between 1 and 360 which are relatively prime to 360 are
96.[ Note that 1 is relatively prime to every positive integer.]
(iv) The coefficient of in
is
(v) If a graph has 6 vertices and 10 edges, then it can’t be regular.
(vi) Peterson graph is bipartite.
(vii) Every edge of a Tree is a bridge.
(viii) The independence number of is
(ix) The DNF of the expression is
(x) The number 8 has atmost one self-conjugate partition.
Let be the number of
Using combinatorial arguments, prove tha where the notation
is used for the number of ways to choose a subset of
Using combinatorial arguments, prove that What is the coefficient of
Check wether the graph in Fig. 1 is Eulerian or not. Is it regular? Justify your answer.
.Solve the recurrence relation using the method of telescopic sums.
A Cantabil showroom offers 7 styles of pants. For each style, there are 10 different possible waist sizes, 6 pants lengths and 4 color choices. How many different types of pants could the showroom have?