Question

a) How many arrangements are there of the word “GRANDMASTER”?

b) Suppose a lottery consists of picking 6 different numbers from 1 to 52. (The order you pick them doesn’t matter). How many possible lottery tickets are there?

Answer 1

the word N = IL (a) Mumba GRAND MASTER of corrangements of Total number letters in the given coord is Repetition letter A mi) = 2 tims Repetition letter R (M2) - 2 times Total mumber of crrangements p - N! where Ny told number letters in a word n! Me! of Mine are number of times letters are refeated 2!2! P = 11x10x 9X8X 7 X 6x5 x 4x 3 x 2x1 4 P = 10 X 10 X 9X8X7X 6X5 X 3X2X1 P 9,979,200 in 52 9,979, 200 number of fossible of possible corrompements existi for the weed GRAND MASTER (b). Total numbers available N= Numbers present on hottery tickets to be ficked up 8 = 6 Since order not considered number of ways can be selected out the required lottery lottery tickets possible the fishing of is so the th which 6 number 52 numbes ore

cond iet is geven 03 , T- N 52. 2C6 cd T= 521 in NI t 6! (52-6)! کیل Y!(N-Y)! T= 52! 6 !X 46! T= 52X SIX SOX 494 48 847 68 5X 4X 34 2XL T = 20, 358, 520 Se thie ore 20, 358, 520 posible Lottay tickets