How can we find out how many 6 digit numbers are there if not allowed and how many 5 element subsets does a,b,c,d,e,f,g,h,i,j have? 1. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions areallowed?6x6 x 6 = 2162. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions arenot allowed?6x5x4120=3. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions arenot allowed, and each list has a W or U in the second entry?5 хоха405. Compute the following:(a) 6!720Section:4. How many 6-digit numbers (using 1,2,3,...,9) are there if repetition is not allowed? Howmany are there which have at least one digit repeated?-10-9:1:2110!(b)7!(c) (12)6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have?10.9.8 = 120 = 7207. Write the expansion of (a + b²)4.94 +4a³b² +6ab4+4ab6+b88. What is the coefficient of r6 in (x+3)7?*The examples, section numbers are from Richard Hammack's "Book of Proof".

As in the text, two Que 4 and 6 are asked t solve. We shall answer one Que only eg 4• it has also…

Answered: 4. How many 6-digit numbers (using…

4. How many 6-digit numbers (using 1,2,3, ... ,9) are there if repetition is not allowed? How many are there which have at least one digit repeated?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

How can we find out how many 6 digit numbers are there if not allowed and how many 5 element subsets does a,b,c,d,e,f,g,h,i,j have?

1. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are
allowed?
6x6 x 6 = 216
2. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are
not allowed?
6x5x4
120
=
3. How many lists of length 3 can be made from the letters U, V, W, X, Y, Z if repetitions are
not allowed, and each list has a W or U in the second entry?
5 хоха
40
5. Compute the following:
(a) 6!
720
Section:
4. How many 6-digit numbers (using 1,2,3,...,9) are there if repetition is not allowed? How
many are there which have at least one digit repeated?
-
10-9:1:21
10!
(b)
7!
(c) (12)
6. How many 5-element subsets does the set {A, B, C, D, E, F, G, H, I, J} have?
10.9.8 = 120 = 720
7. Write the expansion of (a + b²)4.
94 +4a³b² +6ab4+4ab6+b8
8. What is the coefficient of r6 in (x+3)7?
*The examples, section numbers are from Richard Hammack's "Book of Proof".

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