Selection, Distribution & Sequencing: Notes & Examples

BEGINNER

Selection, Distribution & Sequencing: visual worked lesson

Core idea

Selection chooses items, distribution allocates them, and sequencing puts them in order. These are different tasks.

Solving method

Separate selection from arrangement. Translate if-then rules before counting and split into disjoint cases.

Worked example

Three students must each get one of three different books. After choosing a book for the first student, how many books remain? 1. Start with three books. 2. One book is allocated and cannot be reused. 3. Two books remain for the next student.

Read the diagram

A book already given to one pupil is no longer available to the next. After the first assignment, two remain, which answers the example. If all assignments are permitted and both pupils and books are distinct, multiplying the available choices gives six complete assignments. Additional restrictions can reduce this count.

Exam-style application

Choose three members from A,B,C,D,E,F. If A is chosen, B must be chosen; C and D cannot both be chosen. Without A, choose 3 of 5: 10 possibilities, minus C,D with one of B,E,F: 3, leaving 7. With A, B is compulsory and the third member has 4 choices. Total=11. The two cases cannot overlap because one excludes A.

Common mistakes

Check whether items are different and whether reuse is allowed. The rule A implies B does not mean B implies A. Avoid double-counting when cases are not mutually exclusive.

Distinct choices shrink the remaining pool. With no further restrictions: 3 × 2 × 1 = 6 assignments. — Distinct choices shrink the remaining pool

With no further restrictions: 3 × 2 × 1 = 6 assignments. — Distinct choices shrink the remaining pool

Formulas to remember

Unrestricted assignments of n distinct objects = n!

Source record: Bharatiya Pathshala — original illustrated lessons.

BEGINNER

Core idea

Selection means choosing items, distribution means giving items to groups, and sequencing means putting them in order. Read words such as exactly, at least, and at most carefully. They describe different rules.

BEGINNER

Steps

1. Write the available items and places. 2. Translate each rule into a short note. 3. Start with the rule that allows the fewest choices. 4. List possible cases in a tidy way. 5. Cross out every case that breaks even one rule.

BEGINNER

Worked example

Choose two people from A, B, and C. A must be selected. The possible pairs are AB and AC. BC is invalid because A is missing. If B cannot work with A, only AC remains.

BEGINNER

Common mistake

AB and BA are the same selection if order does not matter. They are different only when the two positions have different roles.

Ranking

For a single line with no tied ranks, total people = rank from left + rank from right - 1.

Worked example

A pupil is 7th from the front and 10th from the back. Total pupils = 7 + 10 - 1 = 16; subtract one because the same pupil was counted twice.

Ordering

Ordering uses before/after relations. A partial order may allow several complete orders, so do not invent comparisons.

Worked example

A precedes B and A precedes C. Both A-B-C and A-C-B satisfy the clues. B before C is possible, but not necessary.

Application and strategy

Separate selection from arrangement. Translate if-then rules before counting and split into disjoint cases.

Worked application

Choose three members from A,B,C,D,E,F. If A is chosen, B must be chosen; C and D cannot both be chosen. Without A, choose 3 of 5: 10 possibilities, minus C,D with one of B,E,F: 3, leaving 7. With A, B is compulsory and the third member has 4 choices. Total=11. The two cases cannot overlap because one excludes A.

Common traps and strategy

The rule A implies B does not mean B implies A. Avoid double-counting when cases are not mutually exclusive.

Order, ranking and partial information

Core idea

Represent “A before B” by A→B, and “A taller than B” by A>B. “Not taller” means ≤, not necessarily <. A partial order can leave some pairs incomparable.

Solving method

Record each direct relation, propagate chains, and check for contradictions. A→B and B→C imply A→C, but A→B and A→C do not determine the order of B and C. With distinct ranks in one line, total people = rank from front + rank from back − 1.

Worked example

In a line of 40 people, a person 13th from the left is 40+1−13 = 28th from the right. If H joins before N and K before J, while N and J both precede G and G precedes I, H and K can be candidates for the earliest joiner; they cannot be inferred to be the latest. I must follow G, N, J, H and K, but its order relative to other unconstrained people remains unknown.

Common mistakes

The total is top rank + bottom rank − 1, not their sum. Distinguish a position that is possible in one valid order from a position forced in every order.

Formulas to remember

N = L + R − 1

R = N + 1 − L

Source record: Bharatiya Pathshala — reviewed preparation lessons.

Selection, Distribution & Sequencing, explained simply

Try a small example

Core idea

Steps

Worked example

Common mistake

MAT: Intelligence and Critical Reasoning

CAT: Data Interpretation and Logical Reasoning

CMAT: Logical Reasoning

NMAT: Logical Reasoning

SNAP: Analytical and Logical Reasoning

Selection, Distribution & Sequencing, explained simply

Try a small example

Selection, Distribution & Sequencing: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Core idea

Steps

Worked example

Common mistake

Ranking

Worked example

Ordering

Worked example

Application and strategy

Worked application

Common traps and strategy

Order, ranking and partial information

Core idea

Solving method

Worked example

Common mistakes

Formulas to remember

MAT: Intelligence and Critical Reasoning

CAT: Data Interpretation and Logical Reasoning

CMAT: Logical Reasoning

NMAT: Logical Reasoning

SNAP: Analytical and Logical Reasoning

Selection, Distribution & Sequencing: visual worked lesson

Core idea

Solving method

Worked example

Read the diagram

Exam-style application

Common mistakes

Formulas to remember

Ranking

Worked example

Ordering

Worked example

Application and strategy

Worked application

Common traps and strategy

Order, ranking and partial information

Core idea

Solving method

Worked example

Common mistakes

Formulas to remember