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Updated on: 08 May 2022, 02:55
Originally posted by gmatophobia on 08 May 2022, 00:03.
Last edited by gmatophobia on 08 May 2022, 02:55, edited 1 time in total.
Last edited by gmatophobia on 08 May 2022, 02:55, edited 1 time in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
27% (01:28) correct
73%
(00:54)
wrong
based on 89
sessions
History
Date
Time
Result
Not Attempted Yet
Harry has gone to a store to buy Spiderman toys. If the store sells Spiderman toys in 13 different color-shades, then in how many ways Harry can buy 2 Spiderman toys?
A. 13
B. 26
C. 78
D. 91
E. 156
A. 13
B. 26
C. 78
D. 91
E. 156
Things are not always what they seem; the first appearance deceives many; the intelligence of a few perceives what has been carefully hidden.
-Phaedrus
-Phaedrus
08 May 2022, 01:16
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AbhiroopGhosh
Number of ways of choosing r objects out of n is given by \(^nC_r = \frac{n!}{r!(n-r)!}\)
i.e. Number of ways of choosing 2 toys out of 13 is given by \(^{13}C_2 = 78\)
Answer: Option C
09 May 2022, 01:19
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Official Explanation
Step 1: Understand Question Statement
The store has 13 different color-shades available.
We have to find the number of ways Harry can buy 2 Spiderman toys.
Step 2: Define Methodology
Common Mistake:
Total ways to buy 2 toys = 13C2
Assumption: You may assume we are buying 2 “different” colored toys.
Correct way:
There is a possibility that:
Scenario 1: Harry buys two toys which are of different shade OR
Scenario 2: Harry buys two toys which are of the same shade.
We need to consider both scenarios to find the correct answer.
Step 3: Calculate the final answer
Scenario 1: Harry buys 2 toys of different shades.
This means he has to select 2 shades out of the 13 different shades available for the Spiderman toys.
Thus, number of ways of selecting = 13C2
Scenario 2: Harry buys 2 toys of the same shade
This means he has to select 1 shade out of the 13 different shades available for the Spiderman toys.
Thus, number of ways of selection = 13C1
Thus, the total number of ways of in which Harry can buy 2 toys
= 13C2 + 13C1
= 91
Step 1: Understand Question Statement
The store has 13 different color-shades available.
We have to find the number of ways Harry can buy 2 Spiderman toys.
Step 2: Define Methodology
Common Mistake:
Total ways to buy 2 toys = 13C2
Assumption: You may assume we are buying 2 “different” colored toys.
Correct way:
There is a possibility that:
Scenario 1: Harry buys two toys which are of different shade OR
Scenario 2: Harry buys two toys which are of the same shade.
We need to consider both scenarios to find the correct answer.
Step 3: Calculate the final answer
Scenario 1: Harry buys 2 toys of different shades.
This means he has to select 2 shades out of the 13 different shades available for the Spiderman toys.
Thus, number of ways of selecting = 13C2
Scenario 2: Harry buys 2 toys of the same shade
This means he has to select 1 shade out of the 13 different shades available for the Spiderman toys.
Thus, number of ways of selection = 13C1
Thus, the total number of ways of in which Harry can buy 2 toys
= 13C2 + 13C1
= 91
