Factorials - Simplify [4 (45!) + 46!] / [150 (44!)]

Question:

Simplify [4 (45!) + 46!] / [150 (44!)]

Solution:

[4 (45!) + 46!] / [150 (44!)]

= (4 x 45 x 44!) + (46 x 45 x 44!) / (150 x 44!)

= 44! [(4 x 45) + (46 x 45)] / (150 x 44!)

= ̶4̶4̶!̶ [(4 x 45) + (46 x 45)] / (150 x ̶4̶4̶!̶)

= [(4 x 45) + (46 x 45)] / 150

= [180 + 2070] / 150

= 2250 / 150

= 225 / 15

= 15

Answer:

[4 (45!) + 46!] / [150 (44!)] = 15

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