\f\fQuestion 1 Question 3 Question 4 a. Total number of constants=7 Total number of vowels=5 Since all letters are different Ways of selecting 4 consonants from 7 =7C4=35 Ways of selecting 3 vowels from 5 =5C3=10 total number of groups each containing 4 consonants and 3 vowels =7C4*5C3 =35*10=350 Each group contains 7 letters, which can be arranging in 7P7 distinct ways =7P7 =5040 Therefore required number of words =35*10*5040 =1764000 different words b. Different salads from 5 ingredients Each salad contains at least 2 ingredients Ways of making salad can use 1,2,3,4 or 5 ingredients out of 5 Each ingredient can be present or absent When all are absent there is no salad= 1 instance Making a salad=(2^n)-1 =(2^5)-1 =32-1 =31 salads