How many permutations of the sis, letters A, B, C, D, E, F have B in the last po

Question

How many permutations of the sis, letters A, B, C, D, E, F have B in the last position. Find the number of subset of S [1, 2, .., 7] that obtain the number 4. Academic staff in a department are 25 and 10 The department needs to form a conforming of employees. How many comities are possible? How many comities are possible if the comities must have a facilities and 3 assignment? Each user has a password 8 character long where each character is an uppercase letter, a lower case litter, a digit, or a special character from the set []. How long will it take to check every possible character combination, if each check takes one and second (omega) (1 ns = 1^2 seconds). Show your answer as the approximate number of days. Assume A and B are sets. Suppose |A| = 5 and |B| = 8. Find the number of functions f: A rightarrow B. Suppose |A| = 5 and |B| = 5. Find the number of injective functions f: A rightarrow B. How many terms are there in the binomial expansion of (2/x + x)^10? Find the term without x in the expression (i. e. find the coefficient of x^0). {show all the steps of the calculation}

Explanation / Answer

1.

a. The total number of elements is 6. The last element is always B. So, the remaining five can be altered in any position. So, the number of permutations for the given case is 5! = 120.

b. There will be 2^n subset of a set with n elements.

In the given case there are 7 elements. So, total 2^7 = 128 subsets are available. If we remove element 4 from the set, then only 6 elements will be in set. So, 2^6 = 64 subsets of set without 4. Now the number of subsets with in them is equal to total subsets minus number of subsets without 4 .

= 128 - 64 = 64

Hence, there are 64 subsets for the given set which contains 4 in them.

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