Question

A bag contains $30$ tokens numbered serially from $0$ to $29.$ The number of ways of selecting $3$ tokens from the bag, such that sum of numbers on them is $30$, is

• A. $56$
• B. $75$
• C. $90$
• D. $105$

Answer 1

The correct option is B $75$

Here, order of selection won't matter

one of the coin	other two coins	No. of ways
$0$	$(1,29).....(14,16)$	$14$
$1$	$(2,27).....(14,15)$	$13$
$2$	$(3,25).....(13,15)$	$11$
$3$	$(4,23).....(13,14)$	$10$
$4$	$(5,21).....(12,14)$	$8$
$5$	$(6,19)....(12,13)$	$7$
$6$	$(7,17)...(11,13)$	$5$
$7$	$(8,15)..(11,12)$	$4$
$8$	$(9,13)(10,12)$	$2$
$9$	$(10,11)$	$1$

Hence, required numbe rof ways $=14+13+11+10+8+7+5+4+2+1$
$=75$