Bv a process to be described later, we will randomly form a 7-digit number where
ID: 3051488 • Letter: B
Question
Bv a process to be described later, we will randomly form a 7-digit number where Only the last digit (ones place) can be zero. all 7 digits must be different. * . Consider the sample space S consisting of all possible 7-digit numbers satisfying the above constraints: All 7-cigit numbers sati sfying: S= . all digits different . only the last digit can be zero The sample space above is partitioned (divided or separated) into the 7-digit numbers that end in zero and those 7-digit numbers that do not end in zero All 7-digit numbers sati sfying: . all digits different . last digit is zero All 7-igit umbers satisfying . all digits different . no digits are zero Since the sample space contains literally thousands of elements, it is unreasonable to list them all. It shall be your task to count them:Explanation / Answer
7 digit numbers ending in 0 = 1*9*8*7*6*5*4 = 60480 (1 possibility for last digit, 9 possibilities for 2nd last digit and so on)
7 digit numbers not ending in 0 = 9*8*7*6*5*4*3 = 181440
Total numbers in the set S = 7 digit numbers ending in 0 + 7 digit numbers not ending in 0 = 60480+181440 = 241920
P(7 digit number is odd) = P(last digit is odd) = 5*8*7*6*5*4*3/ 241920 = 100800 / 241920 = 0.4167
P(7 digit number is multiple of 5) = P(Last digit is 0 or 5)
= (60480 + 1*8*7*6*5*4*3)/241920 = 0.333
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