Permutation & Grouped Data Quiz

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Test permutation concepts with grouped data.

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marjorie malana

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Froggy Jumps Permutation & Grouped Data QuizVersión en línea Test permutation concepts with grouped data. por marjorie malana 1 If 5 items are grouped into two colors (3 red, 2 blue), how many distinct orders exist? a 2^5 = 32 b 5! = 120 c C(5;3,2) = 5!/(3!2!) = 10 2 In a survey, 4 categories have counts 2,1,3,4. How many arrangements of labels are possible? a 4! = 24 b (2+1+3+4)! = 10! c 5!/(2!1!3!4!) = 5 3 You have 6 tasks: 2A,2B,2C. How many unique sequences? a 6!/(2!2!2!) = 90 b 3! = 6 c 6! = 720 4 If 7 items are grouped as 3,2,2, what is the number of distinct orders? a 7!/(3!2!2!) = 210 b 7! = 5040 c 3!+2!+2! = 12 5 Interpretation: 10 students split as 4 girls, 6 boys. How many lineups? a (4+6)! = 720 b 10!/(4!6!) = 210 c 10! = 3628800 6 Why does grouping reduce permutations compared to all distinct items? a Groups create more orders b Permutations identical within groups reduce count c Counts increase with groups 7 Given counts 3 red,2 blue,1 green, treat colors as identical within color. How many sequences? a 3!2!1! = 12 b 6! = 720 c 6!/(3!2!1!) = 60 8 If a dataset has 5 categories with counts 1,1,1,1,1, how many sequences? a 5!/(5!) = 1 b (1+1+1+1+1)! = 120 c 5!/(1!1!1!1!1!) = 120 9 Interpretation: A trial has 3 outcomes with frequencies 4,3,3. Number of sequences? a 10! = 3628800 b (4+3+3)! = 10! c 10!/(4!3!3!) = 140 10 Which scenario best uses multinomial counting? a All items distinct b Only two categories c Arranging labeled items with repeated colors/classes

Froggy Jumps

Permutation & Grouped Data QuizVersión en línea

Test permutation concepts with grouped data.

por marjorie malana

If 5 items are grouped into two colors (3 red, 2 blue), how many distinct orders exist?

2^5 = 32

5! = 120

C(5;3,2) = 5!/(3!2!) = 10

In a survey, 4 categories have counts 2,1,3,4. How many arrangements of labels are possible?

4! = 24

(2+1+3+4)! = 10!

5!/(2!1!3!4!) = 5

You have 6 tasks: 2A,2B,2C. How many unique sequences?

6!/(2!2!2!) = 90

3! = 6

6! = 720

If 7 items are grouped as 3,2,2, what is the number of distinct orders?

7!/(3!2!2!) = 210

7! = 5040

3!+2!+2! = 12

Interpretation: 10 students split as 4 girls, 6 boys. How many lineups?

(4+6)! = 720

10!/(4!6!) = 210

10! = 3628800

Why does grouping reduce permutations compared to all distinct items?

Groups create more orders

Permutations identical within groups reduce count

Counts increase with groups

Given counts 3 red,2 blue,1 green, treat colors as identical within color. How many sequences?

3!2!1! = 12

6! = 720

6!/(3!2!1!) = 60

If a dataset has 5 categories with counts 1,1,1,1,1, how many sequences?

5!/(5!) = 1

(1+1+1+1+1)! = 120

5!/(1!1!1!1!1!) = 120

Interpretation: A trial has 3 outcomes with frequencies 4,3,3. Number of sequences?

10! = 3628800

(4+3+3)! = 10!

10!/(4!3!3!) = 140

Which scenario best uses multinomial counting?

All items distinct

Only two categories

Arranging labeled items with repeated colors/classes

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Permutation & Grouped Data Quiz

Froggy Jumps

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Permutation & Grouped Data QuizVersión en línea

por marjorie malana

If 5 items are grouped into two colors (3 red, 2 blue), how many distinct orders exist?

In a survey, 4 categories have counts 2,1,3,4. How many arrangements of labels are possible?

You have 6 tasks: 2A,2B,2C. How many unique sequences?

If 7 items are grouped as 3,2,2, what is the number of distinct orders?

Interpretation: 10 students split as 4 girls, 6 boys. How many lineups?

Why does grouping reduce permutations compared to all distinct items?

Given counts 3 red,2 blue,1 green, treat colors as identical within color. How many sequences?

If a dataset has 5 categories with counts 1,1,1,1,1, how many sequences?

Interpretation: A trial has 3 outcomes with frequencies 4,3,3. Number of sequences?

Which scenario best uses multinomial counting?

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