Question

How many ways can the letters of the word KITCHEN be arranged? How many ways can the letters of the word KITCHEN be arranged if the letters H, E, and N must remain next to each other in the order HEN? If all arrangements of the letters of the word KITCHEN are equally likely, what is the probability that an arrangement will have the letters H, E, and N next to each other in the order HEN? How many ways can the letters of the word PINEAPPLE be arranged? How many ways can the letters of the word PINEAPPLE be arranged if the arrangement must start with the letter A?

Answer 1

☺ KITCHEN PAT Ke 1 Ta] hy N> 7 letters) 1 1 1 E » I Number fo shom t letters can be arx rranged = it 11 ob OS 2 HEN semains Same topeo together in the together as assume HEN single lotter (134) R1 「う 1 - 1 760 G Total seatin s Ale testy Number of ways 5 lettias Can be arranged = 120 3 PCHEN together in order HEN) No, of ways which letters can be arranged if HEN together Total number of ways 120 • 0238 $240

PINEAPPLE p> 3 N-1. L) 1 - 151 A - L Total Letters 9 repeating Letters P3 фче з с ате с No. of Wags of arranging LC —. 2) 2) б - Зодч1 (S) A word sitests from A) А so A is 8 fixed Now in which Letters to be ЗР. 2 2 € are arranged хере has B) 2) 2) 336 о