# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Numbers with Distinct Digits CAT Questions

The question is from Permutation and Combination. Another question which combines number theory with combinatorics. Our task is to find how many odd numbers can be formed under the given conditions . This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 12: How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?

1. 975
2. 960
3. 978
4. 986

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019

##### Method of solving this CAT Question from Permutation and Combination: Numbers that are multiples of 2 and 3 are multiples of 6. Can we say numbers that are multiples of 4 and 6 are multiples of 24?

=> Single digit numbers: 1, 3 or 5: Three numbers
=> Two–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. So, there will be 3 × 5 = 15 such numbers.
=> Three–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. For the 100s’ digit, there are 4 choices {anything apart from what went into the units digit or tens digit}. So, there will be 3 * 5 * 4 = 60 such numbers.
=> 4–digit numbers: There will be 3 * 5 * 4 * 3 = 180 numbers.
=> 5–digit numbers: There will be 3 * 5 * 4 * 3 * 2 = 360 numbers.
=> 6–digit numbers: There will be 3 * 5 * 4 * 3 * 2 * 1 = 360 numbers.

Total number of numbers = 360 + 360 + 180 + 60 + 15 + 3 = 978.

The question is "How many odd numbers with distinct digits can be created using the digits 1, 2, 3, 4, 5 and 6?"

##### Hence the answer is "978"

Choice C is the correct answer.

Signup Now!

###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/-

Next Weekend Batch Starts Sat, Nov 2nd, 2019

###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off

Attend a Demo Class

## CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube

#### Other useful sources for Permutation and Combination Questions | Probability Questions

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com