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# how many odd 7 digit no. can b made from 1,2,2,2,3,3,5. answer with solution .....(answer should come 240)

Uttam Gulshan
31 Points
10 years ago

CONSIDER THE FOLLOWONG :

TO GET ODD NUMBER U MUST HAVE 1 , 5, OR 3 AT THE ONES PLACE.

NOW SUPPOSE THE  ONES PLACE IS FILLED WIH 1, NOW U CAN FILL THE OTHER SIX PLACES IN 6!/3!2! ( SINCE 2 IS REPEATED '3' TIMES AND 3 IS REPEATED '2' TIMES.)

SO NUMBER OF ODD NUMBERS IN THIS CASE= 6!/3!2! =60.

NOW SUPPOSE THE ONES PLACE IS FILLED WITH 3, REST 6 PLACES ARE FILLED IN 6!/3! WAYS ( SINCE 2 IS REPEATED 3 TIMES.)

SO NUMBER OF DIGITS IN THIS CASE=120.

SIMILARLY FOR 5 AT ONES PLACE, NUMBER OF ODD DIGITS=60.

NOW WE CAN FILL THE ONES PLACE BY 1 OR 3 OR 5.

SO BY FUNDAMENTAL PRINCIPLE OF COUNTING, WE GET, NUMBER OF ODD DIGITS = 60 +120+60 = 240.