This Bankers Tutorial article is independent educational material. Examples are illustrative, and changing rules or examination requirements should be checked at the official source.
01 / UNDERSTANDING
Understand the idea
Connect counting to organising a study group: choosing its members and assigning presentation roles are separate decisions with different numbers of outcomes. Counting becomes clearer when the decision being organised is stated precisely. Contrast this with the error of counting restricted cases without first fixing the required member. In a practical demonstration, enumerate a smaller version to check for double counting. Ask the reader to name the controlling fact and explain what additional information would be needed in a different situation, rather than only repeating terminology.
02 / UNDERSTANDING
The concept in context
Counting problems distinguish selecting a group from assigning ordered positions or distinct roles. The method depends on whether exchanging two chosen people creates a new outcome, and whether selections allow repetition or restrictions. Use combinations for unordered selections and permutations for ordered assignments. Apply restrictions before counting, then check that no arrangement has been included twice.
Factorial notation is a compact description, not a substitute for modelling. Identical objects, circular arrangements and designated roles each change what counts as a distinct outcome. A useful study check is to state explicitly what makes two counted outcomes different, then enumerate a smaller version to check for double counting. Explain why the method fits.
03 / UNDERSTANDING
A worked learning case
Five learners are available for a two-person review team. With no roles there are five choose two, or ten, teams. If the team instead needs a coordinator and a recorder, there are five choices for coordinator followed by four for recorder, giving twenty assignments. The same pair produces two different role assignments.
ORIGINAL EDUCATIONAL PRACTICE
Try it before you check.
How many three-person teams can be chosen from six learners when one named learner must belong?
Show the answer and reasoning
10 teams.
The required learner is already selected, leaving two places to fill from the other five learners. Their order does not matter, so the count is five choose two, equal to five times four divided by two, or ten. Counting six choose three would include teams that omit the required learner.
Two traps to watch for.
- Multiplying by extra orders after counting unordered teams.
- Counting restricted cases without first fixing the required member.
YOUR TOPIC-SPECIFIC LEARNING MAP
Turn understanding into practice
State explicitly what makes two counted outcomes different.
Fix required members or blocked positions before applying formulas.
Enumerate a smaller version to check for double counting.
Explain the idea, apply it to a new situation, then check what changed in your reasoning.
BANKERS TUTORIAL · SOURCE NOTES
Keep the source alongside your notes.
Official links provide subject context and authoritative reference material. This guide’s explanation, scenario and question are original Bankers Tutorial learning content.
- www.ibps.in https://www.ibps.in/wp-content/uploads/Detailed-Notification_CRP-PO-XIV_7.8.24.pdf
For IBPS & RRB preparation, check the current official notice before relying on changing dates, rules or examination requirements.
