permutation and combination Question no. 31 In a plane , there are 10 points out of which 4 are collinear , then the number of triangles that can be formed by joining these points are looks_one 60 looks_two 116 looks_3 120 looks_4 None of these Answer Option looks_two 116 Solution Solution : No. of triangles = n C 3 - p C 3 = 10 C 3 - 4 C 3 = 120 - 4 = 116 Question no. 32 The number of straight lines joining 8 points on a circle is looks_one 8 looks_two 16 looks_3 24 looks_4 28 Answer Option looks_4 28 Solution Solution : No. of straight line = n(n-1)/2 = 8 *7 / 2 = 28 Question no. 33 The number of diagonals in a polygon of m sides is looks_one m(m-5)/2! looks_two m(m-1)/2! looks_3 m(m-3)/2! looks_4 m(m-2)/2! Answer Option looks_3 m(m-3)/2! Solution Solution : The number of diagonals in a polygon of m sides is m(m-3)/2! Question no. 34 How many ...

Permutation and Combination Question no. 16 What is the number of three digit odd numbers formed by using the digits 1,2,3,4,5,6 if repetition of digits is allowed ? looks_one 60 looks_two 108 looks_3 120 looks_4 216 Answer Option looks_two 108 Solution Solution : Number of digits at one's place = 1 , 3 , 5 [Total number is 3] Number of digits at ten's place = 6 [1,2,3,4,5,6] Number of digits at hundred place =6 [ 1, 2 , 3 , 4 , 5 , 6 ] Total number of ways = 3 * 6 * 6 = 108 Question no. 17 What is the number of ways of arranging the letters of the word "BANANA" so that no two N's appear together? looks_one 60 looks_two 40 looks_3 80 looks_4 100 Answer Option looks_two 40 Solution Solution : Total no. of ways = 6!/(3!2!) = 60 Two N's come together = 4!*5 / 3! = 20 No. of ways no two N's appear together = 60 - 20 = 40 Question no. 18 How many times does the ...

permutation and combination Question no. 1 how many words can be formed using all the letters pf the words 'NATION' so that all the three vowels should never come together? looks_one 354 looks_two 348 looks_3 288 looks_4 None of these Answer Option looks_3 288 Solution Solution : No. of ways so that all the three vowels should never come together = Total of ways - No. of ways so that all the three vowels should come together = 6!/2! - 3! * 3! * 2 = 288 Question no. 2 In how many ways can the letters of the words 'GLOOMY' be arranged so that the two O's should not be together ? looks_one 240 looks_two 480 looks_3 600 looks_4 720 Answer Option looks_one 240 Solution Solution : Total number of ways so that the two O's should not be together = total no. of ways - no. of ways two O's should be together = 6!/2! - 5 * 4! = 240 Question no. 3 If P(77,31) = x and C(...