Embibe Experts Solutions for Chapter: Arithmetic, Exercise 17: Exercise 17

Three dice, whose all six faces are marked '$1$' to '$6$', are thrown. The number of ways of getting a sum of $16$ is?

After a get-together every person present shakes the hand of every other person. If there were $105$ hands shakes in all, how many persons were present in the party?

A group have $8$ members. Males and females are equal. In how many ways are they arranged in a row to occupy alternate position?

In how many number of ways the letters of the word 'LEADING' can be arranged so that the vowels always come together?

Out of 15 points in a plane, no three points are in a straight line except 5 points which are collinear. How many triangles can be formed?

If the letters of the word $\mathrm{DIRECTOR}$ are arranged in such a way that all the vowels come together. Find out the total number of ways for making such an arrangement.

How many $3$ digit numbers are there with no digit repeated?

In a class there are $26$ boys and $15$ girls. The teacher wants to select a boy or a girl to represent a quiz competition. In how many ways can the teacher make this selection?