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Question Number 122250 by mr W last updated on 15/Nov/20

	Answered by mr W last updated on 15/Nov/20

	$u s i n g g e n e r a t i n g f u n c t i o n m e t h o d$ $t h e n u m b e r o f w a y s i s t h e c o e f f i c i e n t$ $o f t e r m x^{10} i n t h e e x p a n s i o n$ $(C_{1}^{15} x + C_{2}^{15} x^{2} + . . . + C_{15}^{15} x^{15}) \times$ $(C_{1}^{12} x + C_{2}^{12} x^{2} + . . . + C_{12}^{12} x^{12}) \times$ $(C_{1}^{10} x + C_{2}^{10} x^{2} + . . . + C_{10}^{10} x^{10}) \times$ $(C_{1}^{5} x + C_{2}^{5} x^{2} + . . . + C_{5}^{5} x^{5})$ $w h i c h i s 1 032 675 125 .$ $g e n e r a l f o r m$ $G F = \underset{i = 1}{\prod^{m}} (\underset{k = 1}{\sum^{n_{i}}} C_{k}^{n_{i}} x^{k})$
	Commented by mr W last updated on 15/Nov/20

	$i f w e c h o o s e t o t a l l y 4 b o o k s, t h e$ $a n s w e r i s 15 \times 12 \times 10 \times 5 = 9 000 .$ $(= c o e f . o f t e r m x^{4}) ✓$ $i f w e c h o o s e t o t a l l y 5 b o o k s, t h e$ $a n s w e r i s$ $C_{2}^{15} \times 12 \times 10 \times 5 + C_{2}^{12} \times 15 \times 10 \times 5 +$ $C_{2}^{10} \times 15 \times 12 \times 5 + C_{2}^{5} \times 15 \times 12 \times 10$ $= 171 000 .$ $(= c o e f . o f t e r m x^{5}) ✓$
	Commented by mr W last updated on 15/Nov/20

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