Back to the on-screen lesson ·
Apply counting across unfamiliar problems: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Decide whether order matters and whether objects or roles are distinguishable. Handle restrictions through blocks, cases or complements before multiplying possibilities.
How many three-letter arrangements can be made from A,B,C,D without repetition?
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How many committees of three can be chosen from seven people?
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How many distinct arrangements are there of the letters in LEVEL?
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How many four-digit codes use digits 0 through 9 if repetition is allowed and the first digit cannot be zero?
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Five different books are placed in a row. Two named books must be adjacent, in either order. How many arrangements are possible?
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From five women and four men, how many committees contain exactly two women and one man?
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Three shirts, two trousers and four hats are available. An outfit uses one of each, except a particular shirt cannot be paired with one particular hat. How many outfits are allowed?
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How many paths from (0,0) to (3,2) consist only of unit moves right or up?
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How many two-digit positive integers can be made using only 1,2,3,4 without repeating a digit and are even?
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Eight people each shake hands with every other person once. How many handshakes occur?
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How many binary strings of length five contain exactly two ones?
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How many ways can three of eight seats in a row be chosen so that no two chosen seats are adjacent?
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For each counted arrangement, identify one construction path; if two paths yield the same arrangement, the count needs correction.