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# Assignment2(206math)

```Assignment-2
Course: Discrete Mathematics (Math-206)
Marks: 5
Id. Number:______________________
Date of Submission: 18-11-2020 (Wednesday)
Name:_________________________________
Q1.Find the solution of the recurrence relation๐๐ = ๐๐๐
Q2.Solve the recurrence relation ๐๐ = ๐๐๐๐
๐
๐
− ๐๐๐ ๐ where๐๐ = ๐and๐๐ = ๐.
− ๐๐๐๐ ๐ where๐๐ = ๐ and ๐๐ = ๐๐.
Q3.(a).Find the sequence {๐๐ } having the generating function,๐ฎ(๐) =
๐๐
(๐ ๐)๐
๐
+
๐
๐ ๐๐
.
(b). Find the generating function for the sequence ๐๐(๐ + ๐) + ๐ .
Q4. If repetition is not permitted.
(a). How many three digit numbers can be formed from the digit 2, 3, 5, 6 and 9 ?
(b). How many three digit numbers are less than 400 can be formed from the digit 2, 3, 5, 6 and 9 ?
(c). Find the number of distinct permutations that can be formed from all the letters of the word
“PROPOSITION”.
Q5. (a). Find the value of ๐ถ(6, 3).
(b). Show that, ๐ถ(2๐, 2) = 2. ๐ถ(๐, 2) + ๐ .
(c). Find the expansion of (๐ฅ + ๐ฆ) .
(d). Find the coefficient of ๐ฅ ๐ฆ in the expansion of (๐ฅ + ๐ฆ) .
```