For each problem, show all work and explain your reasoning.(a) Does the overall configuration consider the order of the individual pieces of the configuration? (b) Count the number of different configurations for the prompt.1. Passwords of length seven containing distinct letters consisting of uppercase English lettersand/or lowercase English letters2. Committees consisting of four folks formed from the 11 Math faculty members3. Usernames of length six consisting of uppercase English letters, lowercase English letters,and/or numbers from 0–94. Election results from 6 Math 150 students for course president, vice president, and treasurer5. Phone numbers containing only odd numbers6. Social security numbers containing neither 8’s nor 9’s7. Ice cream sundaes consisting of three distinct flavors taken from ten total flavors8. Handfuls of five Skittles consisting of only “warm” colors from a jar containing 8 red, 11green, 7 yellow, 12 purple, and 13 orange9. Possible rolls from fair 6-sided, 8-sided, and 10-sided dice10. Delegations of size four consisting only of folks who prefer hockey or have brown hair selectedfrom folks who took the survey whose results are summarized in the tableFavorite SportFootball (F) Basketball (B) Hockey (H) Blond (D) 11 9 6 26Black (K) 14 13 8 35Brown (W) 12 15 7 34Red (R) 4 5 2 11Total: 41 42 23 10
For each problem, show all work and explain your reasoning.
(a) Does the overall configuration consider the order of the individual pieces of the configuration?
(b) Count the number of different configurations for the prompt.
1. Passwords of length seven containing distinct letters consisting of uppercase English letters
and/or lowercase English letters
2. Committees consisting of four folks formed from the 11 Math faculty members
3. Usernames of length six consisting of uppercase English letters, lowercase English letters,
and/or numbers from 0–9
4. Election results from 6 Math 150 students for course president, vice president, and treasurer
5. Phone numbers containing only odd numbers
6. Social security numbers containing neither 8’s nor 9’s
7. Ice cream sundaes consisting of three distinct flavors taken from ten total flavors
8. Handfuls of five Skittles consisting of only “warm” colors from a jar containing 8 red, 11
green, 7 yellow, 12 purple, and 13 orange
9. Possible rolls from fair 6-sided, 8-sided, and 10-sided dice
10. Delegations of size four consisting only of folks who prefer hockey or have brown hair selected
from folks who took the survey whose results are summarized in the table
Favorite Sport
Football (F) Basketball (B) Hockey (H)
Blond (D) 11 9 6 26
Black (K) 14 13 8 35
Brown (W) 12 15 7 34
Red (R) 4 5 2 11
Total: 41 42 23 10
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