Permutations and Combinations: Selecting a Delegation Quiz — 5 Free Questions

📖 Read the passage, then answer the questions below

A school's student council has 12 eligible members: 7 boys and 5 girls. The council needs to select delegations of various sizes and compositions for different events throughout the year, and wants to know exactly how many distinct delegations are possible in each case.

Separately, the council also needs to arrange 5 distinct trophies in a row on a shelf for the annual awards ceremony, and wants to know how many different arrangements are possible, as well as how many ways a first-place and second-place trophy could be selected and displayed in order on a smaller stand.

Separately again, for a puzzle at the same ceremony, the council wants to know how many distinct codes of different lengths can be formed using the five distinct letters of the word "LEADS", with no letter repeated in any single code.

Question 1

How many ways can a 6-member delegation consisting of all 5 girls together with exactly 1 boy be formed?

Question 2

In how many ways can a President and a Vice-President, two distinct roles, be selected from the 12 members?

Question 3

In how many ways can a 4-member delegation be selected from all 12 members, regardless of gender?

Question 4

In how many ways can a delegation of exactly 1 boy and 2 girls be selected?

Question 5

Consider the following three statements: I. There are 220 ways to select a 3-member delegation from all 12 members. II. There are more ways to select an all-boy 3-member delegation than an all-girl 3-member delegation. III. The 5 distinct trophies can be arranged in 100 different ways. Which of the statements is/are true?

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About Permutations and Combinations: Selecting a Delegation

CLAT's Quantitative Techniques section pairs a short data-rich scenario with several straightforward numeric questions -- here, permutations and combinations applied to a single invented student council scenario, so every answer can be worked out from the figures given, without any outside knowledge.

This quiz is built around one council: twelve eligible members split by gender, five distinct trophies, and a five-letter word, all fully described up front. Every question below is answered using those same figures -- nothing new is introduced question to question.

The twenty-four questions move through the kind of angles CLAT actually tests: selecting delegations with specific gender compositions, arranging distinct objects in order, selecting and arranging a subset in order, ratios between counts, and a multi-statement combination question.

Only five of the twenty-four questions are shown on any single attempt, so replaying this quiz brings a genuinely different mix of angles on the same council rather than the same five memorised by rote.