Cheatsheet: Permutation Combination Probability | General Aptitude for GATE - Mechanical Engineering PDF Download

Answer – c) 20 Explanation : _ _ 5
first two places can be filled in 5 and 4 ways respectively so, total number of 3 digit number = 5*4*1 = 20

Answer – b) 2160 Explanation : Vowels = E, E and A. They can be arranged in 3!/2! Ways so total ways = 6!*(3!/2!) = 2160

Whenever it is not explicity mentioned that fruit and distint, We take them as identical. 0 or more orange can be selected from 4 identical oranges in (4+1)=5 ways. 0 or more apples can be selected from 5 identical apples in (5+1)=6 ways.

0 or more mangoes can be selected from 6 identical mangoes in 7 ways.

∴ Total no. of ways in which all of three types of fruits can be selected (the no. of any type of fruits may also be 0),

5×6×7=210,

But in these 20 selection, there is one selection where all fruits are 0, hence we reduce 1 selection.

∴ the required no. =210−1=209

Answer – c) 91 Explanation : From 15 points number of lines formed = 15c2 6 points are collinear, number of lines formed by these = 6c2 So total lines = 15c2 – 6c2 + 1 = 91

Answer – a) 4! 5! 7! 3!
Explanation : 4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!