SATHEE: Permutations and Combinations 3 Question 1

Permutations and Combinations 3 Question 1

1. The number of 6 digits numbers that can be formed using the digits $0, 1, 2, 5, 7$ and 9 which are divisible by 11 and no digit is repeated, is

(2019 Main, 10 April I)

Show Answer

Answer:

Correct Answer: 1. (a)

Solution:

Key Idea Use divisibility test of 11 and consider different situation according to given condition.

Since, the sum of given digits

$0 + 1 + 2 + 5 + 7 + 9 = 24$

Let the six-digit number be abcdef and to be divisible by 11 , so the difference of sum of odd placed digits and sum of even placed digits should be either 0 or a multiple of 11 means $| (a + c + e) - (b + d + f) |$ should be either 0 or $a$ multiple of 11 .

Hence, possible case is $a + c + e = 12 = b + d + f$ (only) Now, Case I

set $a, c, e = 0, 5, 7$ and $set b, d, f = 1, 2, 9$

So, number of 6 -digits numbers $= (2 \times 2!) \times (3!) = 24$

$[∵ a$ can be selected in ways only either 5 or 7 $]$ .

Case II

Set $a, c, e = 1, 2, 9$ and set $b, d, f = 0, 5, 7$

So, number of 6 -digits numbers $= 3! \times 3! = 36$

So, total number of 6 -digits numbers $= 24 + 36 = 60$

पिछला

अगला

Permutations and Combinations 3 Question 1

1. The number of 6 digits numbers that can be formed using the digits $0, 1, 2, 5, 7$ and 9 which are divisible by 11 and no digit is repeated, is

Answer:

Case II

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Permutations and Combinations 3 Question 1

1. The number of 6 digits numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is

Answer:

Case II

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

1. The number of 6 digits numbers that can be formed using the digits $0, 1, 2, 5, 7$ and 9 which are divisible by 11 and no digit is repeated, is