Fundamental Principle of Counting
Tested in 2 real MPSC questions across 2 years (2015–2016). See it in context on the interactive Concept Graph →
Years it was asked
What you need to know first
Real questions that test this
6 पुरुष व 5 महिला यांच्या गटातून 5 सदस्यीय समिती स्थापन करावयाची आहे. यातून 3 पुरुष व 2 महिला असतील अशी समिती किती प्रकारे तयार करता येईल ? / A five-member committee is to be formed from the group comprising of 6 men and 5 women. In how many different ways can the committee be formed with 3 men and 2 women ?
To form a committee of 3 men and 2 women from 6 men and 5 women, we use combinations. Ways to select 3 men out of 6 is 6C3 = 20. Ways to select 2 women out of 5 is 5C2 = 10. Total ways = 6C3 * 5C2 = 20 * 10 = 200.
दिनूचे घर ते शाळा या दरम्यान 23 बस उपलब्ध आहेत. जर घरापासून शाळेपर्यंत वेगवेगळ्या बसने जाऊन परतायचे असेल तर दिनूला किती पद्धतींनी ये-जा करणे शक्य आहे ? There are 23 buses available between Dinu’s house and his school. How many ways are possible for Dinu to go from his house to school and return using different buses ?
Dinu has 23 buses to go from house to school. To return using a *different* bus, he has 22 options available. Total ways = 23 * 22 = 506.