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Q.

Thirteen persons are sitting in a row. Number of ways in which four persons can be selected so that no two of them are consecutive is equal to ____

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a

number of ways in which all the letters of the word “M A R R I A G E” are permutated if no two vowels are never together.

b

number of numbers lying between 100 and 1000 using only the digits 1,2,3,4,5,6,7 without repetition.

c

number of ways in which 4 alike chocolates can be distributed among 10 children so that each child getting at most one chocolate.

d

number of triangles can be formed by joining 12 points in a plane, of which 5 are collinear

answer is B, C, D.

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Detailed Solution

x1+x2+x3+x4+x5=9,x1,x50

x2,x3,x41,

x1+(x2-1)+(x3-1)+(x4-1)+x5=6

 number of solutions are  10C4= 210

A) 5 × 12 × 12 = 720  (B) 7P3=210

 C) 10C4=210  D) 12C35C3=210

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