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d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n - k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (2) + ² (7) + ²² (²) + 2³ (²) + 2¹ (") +2 = 3¹.

d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n - k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (2) + ² (7) + ²² (²) + 2³ (²) + 2¹ (") +2 = 3¹.

Advanced Engineering Mathematics
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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Could you please help me with sections D,E,F,G please?

Let's count ternary digit strings, that is, strings in which each digit can be 0, 1, or 2. a. How many ternary digit strings contain exactly n digits? b. How many ternary digit strings contain exactly n digits and n 2's. c. How many ternary digit strings contain exactly n digits and n - 1 2's. (Hint: where can you put the non-2 digit, and then what could it be?) d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n – k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (6) + ² (7) + 2² (2) + 2³ (3) +... 2² (1) +2 = 3¹. =
Transcribed Image Text:Let's count ternary digit strings, that is, strings in which each digit can be 0, 1, or 2. a. How many ternary digit strings contain exactly n digits? b. How many ternary digit strings contain exactly n digits and n 2's. c. How many ternary digit strings contain exactly n digits and n - 1 2's. (Hint: where can you put the non-2 digit, and then what could it be?) d. How many ternary digit strings contain exactly n digits and n - 2 2's. (Hint: see previous hint) e. How many ternary digit strings contain exactly n digits and n – k 2's. f. How many ternary digit strings contain exactly n digits and no 2's. (Hint: what kind of a string is this?) g. Use the above parts to give a combinatorial proof for the identity (6) + ² (7) + 2² (2) + 2³ (3) +... 2² (1) +2 = 3¹. =
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