Seven blank spaces, which are numbered from 1 to 7, are arranged in a row in ascending order from left to
right. Two A's three B's and two C's are to be filled in these seven blank spaces such that the same
alphabet never consecutive blank spaces. In how many ways can this be done if B is always filled in the first
blank space?
Answers
Answer:
two A's three B's and c's
Step-by-step explanation:
i
Given : Seven blank spaces, which are numbered from 1 to 7, are arranged in a row in ascending order from left to right.
Two A's three B's and two C's are to be filled in these seven blank spaces such that the same alphabet never consecutive blank spaces
To Find : In how many ways can this be done if B is always filled in the first
blank space
Solution:
As B is 1st Hence
BA or BC is only possible
considering BA cases then BAB or BAC is possible
BAB
BABA BABC
BABACBC BABCABC , BABCACB , BABCBAC , BABCBCA
BAC
BACA BACB
BACABCB BACBACB , BACBABC , BACBCAB ,BACBCBA
Considering BC cases then BCA or BCB is possible
BCA
BCAB , BCAC
BCACBAB , BCABABC , BCABACB , BCABCAB , BCABCBA
BCB
BCBA , BCBC
BCBCABA , BCBABAC , BCBABCA , BCBACAB , BCBACBA
Hence total 20 possible
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