find the number of four letter arrangements of the letter of the word shoot how many of them begin with o
Answers
Given : SHOOT
To Find : number of four letter arrangements of the letter of the word shoot
how many of them begin with O
Solution:
Case 1 : Both O are selected
Number of ways = ³C₂ = 3
4 Letters can be arranged in 4!/2! = 12 ways
Total ways = 3 x 12 = 36
Starting with
O - rest 3 Letters can be arranged in 3! = 6 Ways
Ways to start with O = 3 x 6 = 18
Case 2 : only one O is selected
Number of ways = ³C₃ = 1
4 Letters can be arranged in 4! = 24 ways
Starting with
O - rest 3 Letters can be arranged in 3! = 6 Ways
Total Possible combination = 36 + 24 = 60
Starting with O = 18 + 6 = 24
Total = 60
24 Begins with O
Direct method to finding starting with O
1st letter O
Rest 3 letters out of 4 can be selected in ⁴C₃ = 4 ways
and 3 letters can be arranged in 3! = 6 wats
4 x 6 = 24
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