Given that x + y + z + t = 30. Match the number of solutions to this equation in List-II with constraints placed on x, y, z, t in List-I.

Question

Given that $x + y + z + t = 30$ . Match the number of solutions to this equation in List-II with constraints placed on $x, y, z, t$ in List-I.

	List-I		List-II
P)	$x, y, z, t \in I; x \geq - 1, y \geq 3, z \geq 5, t \geq 0$	I)	585
Q)	$x, y, z, t \in I; x \geq 0, 2 \leq y \leq 7, 4 \leq z \leq 8, t \geq 1$	II)	680
R)	$x, y, z, t \in W and x, y are odd while z, t are even$	III)	816
S)	$x, y, z, t \in N and t is a multiple of 5$	IV)	580
		V)	2600

The correct option is:

Smart Achievers · Accepted Answer

(1)

$(P) {}^{28}C_{3} = 2600$

$(Q) {}^{26}C_{3} - {}^{20}C_{3} - {}^{21}C_{3} + {}^{15}C_{3} = 585$

$(R) {}^{17}C_{3} = 680$

$(S) {}^{24}C_{2} + {}^{19}C_{2} + {}^{14}C_{2} + {}^{9}C_{2} + {}^{4}C_{2} = 580$

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