Applying Permutations in Context (Advanced)

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1) How many 5-letter arrangements can be made from the letters in the word "ALGEBRA" if no letter repeats?

Explanation

(7 distinct letters total, so 7P5 = 7×6×5×4×3 = 2520.)

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About This Quiz
Applying Permutations In Context (Advanced) - Quiz

Ready for the next level? In this quiz, you’ll face advanced permutation problems that stretch your logical and computational skills. Take this quiz to push your understanding further and tackle challenging real-world applications of permutations.

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2) How many ways can 4 students be seated in a row of 8 chairs?

Explanation

(8P4 = 8×7×6×5 = 1680.)

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3) How many different lineups of 5 runners are possible if there are 9 total runners?

Explanation

(9P5 = 9×8×7×6×5 = 15,120.)

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4) A security code consists of 3 different letters followed by 2 different digits. How many codes are possible?

Explanation

(26P3 × 10P2 = 26×25×24 × 10×9 = 1,560,000.)

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5) How many ways can 4 different paintings be arranged on a wall if two specific paintings must stay together as a unit?

Explanation

(Treat the 2 as one unit → 3 objects total → 3! = 6 ways. But the pair can switch order internally → ×2 = 12.)

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6) How many 5-letter codes can be formed from the alphabet if repetition is allowed?

Explanation

(26⁵ = 11,881,376.)

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7) A locker combination uses 3 letters followed by 3 digits. Letters cannot repeat, but digits can. How many combinations are possible?

Explanation

(26P3 × 10³ = 26×25×24 × 1000 = 158,184,000.)

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8) From a group of 10 people, how many different 6-person lineups can be formed?

Explanation

(10P6 = 10×9×8×7×6×5 = 151,200.)

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9) How many different ways can the letters in the word “ALGEBRA” be arranged?

Explanation

(The word ALGEBRA has 7 letters with “A” repeated twice → 7!/2! = 5040/2 = 2520.)

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10) How many different ways can 6 students stand in a single line if the tallest student must be in the middle?

Explanation

(Fix the tallest in position 3. That leaves 5 students to arrange in the remaining 5 spots: 5! = 120.)

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How many 5-letter arrangements can be made from the letters in the...
How many ways can 4 students be seated in a row of 8 chairs?
How many different lineups of 5 runners are possible if there are 9...
A security code consists of 3 different letters followed by 2...
How many ways can 4 different paintings be arranged on a wall if two...
How many 5-letter codes can be formed from the alphabet if repetition...
A locker combination uses 3 letters followed by 3 digits. Letters...
From a group of 10 people, how many different 6-person lineups can be...
How many different ways can the letters in the word “ALGEBRA” be...
How many different ways can 6 students stand in a single line if the...
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