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Asked by suchananag2002 15th February 2020, 10:24 AM
Answered by Expert
Answer:
To find the number of natural numbers which are smaller than 2 x 108 and which can be written by means of the digits 1 and 2.
O n e space d i g i t space n u m b e r s space space minus space 1 comma space 2 space rightwards double arrow T o t a l space c h o i c e s space equals space 2
T w o space d i g i t s space n u m b e r s space minus space 11 comma space 12 comma space 21 comma space 22 space rightwards double arrow space N o. space o f space 2 space d i g i t s space n u m b e r space equals space 4 space equals space 2 to the power of 4
T h r e e space d i g i t s space n u m b e r s space minus space 111 comma space 112 comma space 121 comma space 122 comma space 211 comma space 212 comma space 221 comma space 222 space rightwards double arrow space N o. space o f space 3 space d i g i t s space n u m b e r s space equals space 8 space equals 2 cubed
vertical ellipsis
N o. space o f space 8 space d i g i t s space n u m b e r s space equals space 2 to the power of 8
A s space 2 cross times 10 to the power of 8 space h a s space 9 minus d i g i t s comma space s o space w e space n e e d space t o space f i n d space u p space t o 2 cross times 10 to the power of 8
N o. space o f space 9 space d i g i t s space n u m b e r s space equals space 2 to the power of 9 over 2 equals 2 to the power of 8
T o t a l space n o. space o f space n u m b e r s space equals space 2 plus 4 plus 8 plus 16 plus 32 plus 64 plus 128 plus 256 plus 256 equals 766
Answered by Expert 18th February 2020, 11:27 AM
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