Sequences and S...

In a combination, the ordering of the selected objects is immaterial whereas in a permutation, the ordering is essential.

There are $6$ boxes numbered $1, 2 ....... 6$. Each box is to be filled up either with a red or a green ball in such a way that at least $1$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

Rajdhani Express going from Bombay to Delhi stops at five inter-mediate stations, $10$ passengers enter the train during the journey with $10$ different ticket of two classes. The number of different sets of tickets they may have is

Find the area of the triangle whose vertices are $(3,2), \ (-2, -3)$ and $(2,3)$.

Find the area of the right-angled triangle whose vertices are $(2, -2)$ , $(-2, 1)$ and $(5, 2).$

Observe the given multiples of 37.
${37\times3=111}$
${37\times 6 =222}$
${37\times9=333}$
${37\times12=444}$-------------------------------
Find the product of ${37\times27}$

Consider the points $A( a, b + c)$, $B(b, c + a)$, and $C(c, a +b)$ be the vertices of $\bigtriangleup$ABC. The area of $\bigtriangleup$ABC is:

$(3, 1), (-3, 2)$ and $\displaystyle (0,2-\sqrt{3})$ are the vertices of __________ triangle of area ___________.

Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are $(2,2)$, $(4,4)$ and $(2,6)$.

Find the area of the triangle whose vertices are $(a, b + c), (a, b - c)$ and $(-a, c)$.