Permutations - Learning Materials

Find Itu number of a letter words, with or without meaning which can be formed out of It letters of Itu word ROSE, where repetition of letters is no allowed. First place - 4 different ways ind place - 3 1. namber of four letter words forme el 4 x 3 x 2 x 1 = 2-digige digit even num • Hoe om any digging can be formed from Itu digits 12; 3; 4 and 5. if ltm digits a be repeated. First plove-5 second place -2 Total number of & digit even numbes = 3) How many 3-digit numbers can formed from the digits 1,2,3,4 assuming that. repetition of the digits ⅰ) repe tiflon allowed is ⅰ) repetition of lto digits is not allowed? pot place - 5 different ways. ind place - Wrd place total numbes of 3 digid numbess formed 125 ways $st place - 5 differnt ways. And place-4 ipped place -3 Total number 3 digit formed numbers - Go ways 4) How many or digit telephone numbers Con be 5- Constructor using lte digit oto 9 if each number starts with 67 and ence? no digit appears more than87 0,4,2,3,4,5, wrd plove wth place - 8 different ways -7 12 . Total number of 5 digit telephone numbers = 8 x 7 x 6 336 5) Given 5 flags of different colours how many different signals can be generated if each signal Itu othes. use of equire aflags, one below way 4 way upper part - 5 different ways louser past -4 :. number of different signals for med 5x4 =20 ways Factorial notation The factorial of a natural numbes n is the continued Produd of the first in natural numbers. ie, n! =1x2x 3x..xn oes n 5/ = 1 x 2 x 3 x 4 x 5 = 21=1×2= 31=1x2x3= Note