Question

Show your calculations. (2 marks) How many five-digit numbers can be formed from the set of nine number 3, 4, 5, 6, 7, 8} if no number is repeated and no number starts with a zero, and a) there are no other restrictions? (2 marks) b) the result must be an odd number? (3 marks) Show your calculations. (5 marks total)

Answer 1

Guren deguts - 0, 1, 2, 3, 4, 5, 6, 7, 8. number of dégâts (n) = 7 As, 5 dégât numbers to be formed = 5 Now, lumbers of fire - digit numbers, Pon! in-r)! 9! (9-5)! 4! 3x8x7x6x5x40 = 15,120

Now, these total numbers include the fire - digit numbers which starts with zero, for this we need to deduct the numbers which are started with zero. Fire-digit numbers starts with zero' P = n! (n-r)! where, n - - 1 - 8 = 4 r = 5-1

Requirement - a & Total numbers of fire-dégât numbers - 15,120 – 1680 e 13,440 Ans Odd numbers of 5 digits using the given digits can be formed by placing I' or 3 or 5 oz t at the unit place Now, if we place 1 at the unit place numbers, of odd numbers - P (8,4) – P (7,3) or epey - Bz 81 7! (8-4)! (7-3) 8x7x645x4T - 7*6+5 x 48 4 47 3 1680 – 210 – 1,470 o odd numbers starts with zero es excluded. Similarly, if we place 3 at the unit place Number of odd numbers = 8Pu - P2 = 1470

vast Semelarly, ef we place 5 at the place number of odd numbers. - Pu - 7 - 1470 Agaur. ef we dlace 7 at the unst number of odd numbers - Spu783 - 1470 place Requirement – b o Total number of odd numbers 1470 +1470 + 1470 + 1470 - 5880 Ang For better understanding. Total five digit numbers: ? ? ? ? ? = = 15,120 Total tire dédit numbers starts with zero 0 ? ? ? ? - spy = 1680 odd numbers l'ozg'o25'027 Spa - 1680 1680 odd numbers starts with zero o ? ? ? 43/5/7 EP: 210