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 $$(-a, c)$$.