Question

PLEASE DO BOTH

(7) (5 pts) A croissant shop has plain croissants, cherry croissants, chocolate croissants, almond croissants, apple croissants, and broccoli croissants. How many ways are there to choose (a) a dozen croissants? (b) two dozen croissants with at least two of each kind? (8) (5 pts) How many solutions are there to the equation 11 +12+13 +In+ 15 + 16 = 29, where I, for i = 1,2,3,4,5,6, is a non-negative integer such that (a) Ii > 1 for i = 1, 2, 3, 4, 5, 6? (b) 21 > 1, 12 > 2, I3 > 3,14 > 4,25 > 5, and xe > 6?

Answer 1

& Gover Some Goussants 6 deftepnt types of croissants a) choosing a dozen Gaissant Clad choosing 6 from 12 c Combinations) 1226 - 3 u 12! 6! X6! 12X11XIOXX X8X7 6x5x1x2x2 - 11X3xUxz - 33 x 28 - 924 b two dozen Gaisant with at least two of each kind! L 24 = atleast one of each kund = Cannot be possible as ody 6 Varieties age there 2406 2) OG+xzt az txutx+x6 =29. as for oil Cxi 180 at Cannot be possible

= 180 Combination (Solutions x + x₂ + 3G + xy +*+*6 = 23 29 هدد «درة «درة 296 = 2 +که+ہلا+ه+ره+ه مل د-را-بترو)c دد cC98 جديد راديه رده رد به راه (ط کی گ۔۔۔ -290دة +لا+ہلا+د+ردة .. د - 5 - 29 - 6-3 ر4+ C2 دی cC18 and x6 ²6 G+ x + 2z+xy tasta= 13
use combinations u get the result